Ruby, 45 bytes

->n{([*?a..?z,*?A..?Z,*0..9]*n).sample(n)*''}

Try it online!

Java 8, 183 149 97 88 87 bytes

n->{for(int t;n-->0;t*=Math.random(),System.out.printf("%c",t+=t>9?55+t/36*6:48))t=62;}

Try it online.

-9 bytes by porting @2501's C answer, so make sure to upvote him as well!
-1 byte thanks to @ceilingcat

Explanation:

n->{                           // Method with integer parameter and String return-type
  for(int t;                   //  Temp integer
      n-->0                    //  Loop the input amount of times:
      ;                        //    After every iteration:
       t*=Math.random(),       //     Set `t` to a random integer in the range [0,62)
       System.out.printf("%c", //     Print as character:
         t+=                   //      The random integer, after we've added:
            t>9?               //       If the random integer is larger than 9:
             55                //        Add 55
             +t/36             //        And if the random integer is larger than 35:
              *6               //         Add an additional 6
            :                  //       Else:
             48))              //        Add 48
    t=62;}                     //   (Re)set `t` to 62 for the random

Google Sheets, 78 bytes

=JOIN(,SORTN({ROW(1:10)-1;CHAR({ROW(65:90);ROW(97:122)})},A1,,RANDARRAY(62),))

Swift, 138 127 124 115 98 bytes

let s={(1...$0).map{_ in.init(.init([48...57,65...90,97...122].joined().shuffled()[0]))}.joined()}

Uiua ^SBCS, 26 bytes

⊏⌊×62∵⋅⚂⊚:⊂+@0⇡10⊂⌵.+@a⇡26

Try it!

⊏⌊×62∵⋅⚂⊚:⊂+@0⇡10⊂⌵.+@a⇡26
                    +@a⇡26  # lowercase alphabet
                 ⊂⌵.        # join uppercase alphabet
          ⊂+@0⇡10           # join digits
        ⊚:                  # create array of length n
     ∵⋅⚂                    # fill with random numbers in [0, 1)
  ×62                       # times 62
 ⌊                          # floor
⊏                           # select

Ruby -rsecurerandom, 32 bytes

->n{SecureRandom.alphanumeric n}

Attempt This Online!

J-uby -rsecurerandom, 26 bytes

:alphanumeric&SecureRandom

Attempt This Online!

Scala 3, 123 bytes

A port of @Kevin Cruijssen's Java answer in Scala.

Golfed version. Attempt This Online!

n=>{var t=62;for(_<-0 to n-1){t=(t*scala.math.random).toInt;if(t>9)t+=(if(t>35)61 else 55)else t+=48;print(t.toChar);t=62}}

Ungolfed version. Attempt This Online!

object Main {
  trait N {
    def c(n: Int): Unit
  }

  val n: N = (n: Int) => {
    var t = 62
    for (_ <- 0 until n) {
      t = (t * scala.math.random()).toInt
      if (t > 9) t += (if (t > 35) 61 else 55) else t += 48
      print(t.toChar)
      t = 62
    }
  }

  def main(args: Array[String]): Unit = {
    for (_ <- 1 to 3) {
      n.c(5)
      println()
      n.c(10)
      println()
      n.c(20)
      println()
      n.c(33)
      println()
      println()
    }
  }
}

Vyxal, 18 bits^v2, 2.25 bytes

krƈ

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What can I say, there's a built-in for choosing n random characters from a string.

Explained

krƈ
  ƈ  # Choose n random characters from
kr   # the string 0-9a-zA-Z

Thunno 2 J, 4 bytes

ıkȦɼ

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Explanation

ıkȦɼ  # Implicit input
ı     # Input number of times:
 kȦ   #  Push [a-zA-Z0-9]
   ɼ  #  Random choice
      # Implicit output

PowerShell, 56 bytes

param($n)-join((0..9+'a'..'z'+'A'..'Z')*$n|random -C $n)

Try it online!

Javascript, 83 bytes

f=n=>n?f(--n)+String.fromCharCode((k=Math.random()*62|0)+(k<10?48:(k<36?87:29))):''

Explained:

f=n=>  //Define function, n =  string length
n?      // if n is not falsy (0)
f(--n)+ //return f(n-1) (1 char shorter) plus
String.fromCharCode( // the character of
(k=Math.random()*62|0) //random number between 0 and 62 (num of chars)
+(
k<10?          //plus, if k < 10 (char is number)
48             //k + 48
:(k<36?        //else, if k < 36 (char is lowercase)
87             //k + 87
:29)           // else k + 29
) 
)
:''   //if n is falsy, return empty string.

The numbers (48,29,etc) come from lining the charcodes up: |char|num|charcode|num - charcode| | - | - | - | - | | 0 | 0 | 48 | 48 | | 1 | 1 | 49 | 48 | | ... | ... | ... | ... | | 9 | 9 | 57 | 48 |

So random + 48 for numbers. For lowercase,

so rand + 87, and for uppercase, |char|num|charcode|num - charcode| | - | - | - | - | | A | 36 | 65 | 29 | | B | 37 | 66 | 29 | | ... | ... | ... | ... | | Z | 61 | 90 | 29 |

Zsh, 33 bytes

tr -dc a-zA-Z0-9</*/ur*|head -c$1

Try it online!

05AB1E, 4 bytes

žKãΩ

Try it online! Times out on TIO for inputs \$>3\$, but it does work in theory.

žKãΩ  # full program
   Ω  # random element from...
žK    # "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"...
  ã   # to the cartesian power of...
      # implicit input
      # implicit output

Alternative, 4 bytes

žLãΩ

Try it online!

žLãΩ  # full program
   Ω  # random element from...
žL    # "zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA9876543210"...
  ã   # to the cartesian power of...
      # implicit input
      # implicit output

APL (Dyalog Extended), 17 bytes

Full program. Prompts for length.

(?⎕⍴62)⊇⎕A,⎕D,⌊⎕A

Try it online!

⎕A uppercase Alphabet

⌊ Lowercased

⎕D, prepended by the Digits

⎕A, prepended by the uppercase Alphabet

(…)⊇ select the following indices from that:

 ⍴62 reshape 62 to the following shape:

 ⎕ prompt for a number

 ? random indices in in those ranges

Japt, 12 8 bytes

;BiCí)öU

Try it

Alchemist, 577 689 bytes

Contains a line for every character [0-9A-Za-z]:

_->In_n
n->Out_"0"
...
n->Out_"9"
n->Out_"A"
...
n->Out_"Z"
n->Out_"a"
...
n->Out_"z"

Input from stdin, try it online!

Explanation

The universe of Alchemist will start with one _-atom, so the only thing that can happen is to read the number of n-atoms. Then one of the remaining rules will be matched pseudo-uniformly at random until no n-atoms remain.

PHP, 51 bytes

while($argn-=ctype_alnum($c=chr(rand()))&&print$c);

Run as pipe with -nR or try it online.

Sinclair ZX81/Timex TS1000/1500 BASIC, ~63 tokenized BASIC bytes

 1 INPUT N
 2 IF NOT N THEN STOP
 3 FOR N=SGN PI TO N
 4 PRINT CHR$ (CODE "A"+RND*26);
 5 NEXT N

There are no lower-case characters in ZX81 without using assembly or having some sort of UDG ROM or something, and for the time being, it only outputs A-Z. If zero is entered then the program halts and returns to direct mode.

Pip, 13 bytes

LaORCz.AZ.J,t

Try it online!

Explanation

               a is cmdline arg; t is 10; z is lcase alphabet; AZ is ucase (implicit)
La             Do the following, a times:
  O             Output (without newline)
   RC           random choice from:
     z           Lowercase letters
      .AZ        concatenated with uppercase letters
         .J,t    concatenated with range(10) joined into a string

APL NARS, 65 bytes, 35 chars

{(⍵≤0)∨⍵≥1E6:''⋄t[?¨⍵⍴⍴t←⎕A,⎕a,⎕D]}

As usual here do not is specificied the range of validity for the function... I agree in check for range but not agree 100% in checking the type, because some time is possible one extention for one function (possible not in this case). Test:

  g←{(⍵≤0)∨⍵≥1E6:''⋄t[?¨⍵⍴⍴t←⎕A,⎕a,⎕D]}
  g ¯2000000

  g 0

  g ¯3

  g 23
86uSfWH1zfpj4JE439he9Jp
  g 3
ueQ
  g 2
l3
  g 1
M
  g 100
pkHi07YmFmZpr9TpUNCIEtQf20CURGszkP2LvzgpnfaZTKPg3nYvo4PK0Rg
  1cMxcjSRGWLrtf1RP8NEC3HlIcjW6TqfSOdqmrSqu

Python 2, 79 83 79 bytes

import random as r,string as s;lambda x:''.join(r.sample(s.printable[:62]*x,x))

+4 bytes (didn't account for repetition)

-4 bytes (Thanks to @Rod for the suggestion for using printable[:62])

C#, 214 177 bytes

Sorry to embarrass myself like this but:

void q(){int k=int.Parse(Console.ReadLine());Random r=new Random();for(;k>0;k--){Console.Write((char)(r.Next(1,4)>2?r.Next(1,3)>1?r.Next(97,123):r.Next(48,58):r.Next(65,91)));}}}}

Shaved some bytes off due to suggestion to just make it a function.

Bash, 43 bytes

shuf -ern$1 {a..z} {A..Z} {0..9}|tr -d "\n"

Try it online!

PowerShell, 58 54 Bytes

-4 thanks to Andrei Odegov - casting to a char array instead of looping to create a char array.

-join[char[]](65..90+97..122+48..57|random -C "$args")

generates a range 1..2+4..5 = 1,2,4,5 of all the acceptable charachter codes, then selects $args number of elements randomly using random -Count - the resulting elements are looped through |%{} and turned into [char]s, are cast to an array of chars using [char[]] - then the whole thing is encapsulated in brackets and -joined together.

PS C:\users\sweeneyc\Desktop> .\grstr.ps1 5
oaCE5
PS C:\users\sweeneyc\Desktop> .\grstr.ps1 10
UReh6McG7D
PS C:\users\sweeneyc\Desktop> .\grstr.ps1 30
t1YrhZf5egyzqnPlWUKV3cEoIudMTs

Does not work for an input of 0 as Get-Random only accepts numbers above 1 for the -Count parameter.

C, 54 52 bytes

• -2 bytes, thanks to @RosLuP

Try Online

i;f(n){n&&f(n-(isalnum(i=rand()%128)&&putchar(i)));}

Axiom, 150 bytes

f(x:NNI):Union(String,Complex INT)==(x>9.E8=>%i;c:=alphanumeric()::String;r:="";repeat(x=0=>break;x:=x-1;w:=1+random()@INT rem 62;r:=concat(c.w,r));r)

i find repeat( ...break...) the most versatile type of loop in Axiom as for(;;) in C. I find functions without some think or reflection on their input only danger toys

   [0,""]
   [1,"t"]
   [2,"rT"]
   [10,"fcCOgd2aoP"]
   [100,
    "byFH5ikoQTIEA3TdJ4thNueA0vuowxz5PC7N1yUEgZUkuddjfwbRjYMim1mAYzLhZ8hDJskOUZ
    SckbflbU1ZL2q0KTWUMF9dx6jX"
     ]
   [10000000000000000,%i]

Clojure, 80 bytes

#(apply str(for[i(range %)](char(rand-nth(mapcat range[48 97 65][57 122 90])))))

I guess the only smart part is building that set of ASCII integer values.

Lua, 105 98 bytes

s,n="",io.read()while#s<n do c=s.char(math.random(48,122))s=s..(c:match"%w"and c or'')end print(s)

Generate any character between 48 and 122, if alphanumeric, add to output string. When output string is length n, stop and output.

Edit: Saved 7 bytes thanks to suggestions from Josh.

Jelly, 5 bytes

Missed a trick - see ais523's 4 byter

ØBX$€

Try it online!

How?

ØBX$€ - Main link: n
    € - for each in range(n):
   $  -   last two links as a monad:
ØB    -     "base digits" - yields list of chars "01..9AB...Zab...z"
  X   -     random choice

C# - 121 bytes

void g(int n){Console.Write(Convert.ToBase64String(System.Text.Encoding.UTF8.GetBytes(new Random().Next().ToString())).Substring(0,n));}

CJam, 18 bytes

ri{;'],_el^9,+mR}%

Explanation:

ri   e# Read integer
{    e# For each (loops from 0..n-1):
 ;   e#   Delete the index from the top of the stack
 '], e#   Get all the characters 0x00 to 0x5b ("[")
 _el e#   Duplicate and convert letters to lowercase
 ^   e#   Symmetric set difference - this keeps only
     e#     uppercase and lowercase letters
 A,+ e#   Add all the digits into this string
 mR  e#   Random choice of one element in the array
}%   e# End for loop
e# Implicit output

C, 67 Bytes

c;f(n){char b[1],*p=b+64;for(;n;)isalnum(c=*p++)?putchar(c),n--:0;}

Try it online

I'm getting some strange results - keep on hitting the run button - feels like I'm a character in Lost:

PoPPmyE79hmy
arcPaTasITJK
PCFaniHSAKPS
yPytyxQoAKMA
DOPrgDONeDO8
...

Can anyone explain why there is always a 'P' or 'p' in the output?

PHP, 56 Bytes

for(;$argn;)ctype_alnum($l=chr(rand()))&&$argn-=print$l;

Online Version

ctype_alnum

Pyth, 7 11 bytes

O^s++rG1GUT

Try it online

Explanation

O^s++rG1GUT
    +rG1G      Take the uppercase and lowercase alphabets.
   +     UT    Add it to the list [0, ..., 9].
  s            Concatenate to get a string.
 ^         Q   Get all strings of length N.
O              Choose one at random.

Pyke, 4 bytes

~JfH

Try it online!

~J   -   "0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
  f  -  cominbations(^, length=input)
   H - random.choice(^)

Batch, 175 bytes

@set s=0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz
@for /l %%i in (1,1,%1)do @call :c
@echo %s:~62%
:c
@set/an=%random%%%62
@call set s=%s%%%s:~%n%,1%%

s performs double duty here as it contains both the alphanumeric list and the randomly selected characters. After printing the result the code falls through to the subroutine whose result is ignored.

Jelly, 4 bytes

ØBṗX

Try it online!

Explanation

ØBṗX
ØB     All letters (uppercase and lowercase) and digits
  ṗ    Cartesian power with {the input}
   X   Select a random possibility

Cartesian power basically generates all list of a given length that can be formed out of a given set of elements; that's exactly what we need here.

Mathematica 66 Bytes

""<>Cases[1~CharacterRange~122,_?LetterQ|_?DigitQ]~RandomChoice~#&

which is a little bit shorter than using the WordCharacter pattern with StringCases

Python + exrex, 81 bytes

import exrex,random
lambda n:random.choice(list(exrex.generate("[A-Za-z0-9]"*n)))

Taxi, 2577 bytes

Go to Post Office:w 1 l 1 r 1 l.Pickup a passenger going to The Babelfishery.Go to The Babelfishery:s 1 l 1 r.Pickup a passenger going to Sunny Skies Park.Go to Sunny Skies Park:n 1 l 1 l 1 r.[a]Go to Heisenberg's:n 1 r 1 r 3 r.Pickup a passenger going to Cyclone.Go to Go More:n 1 l 3 l 3 l.Go to Starchild Numerology:e 2 r.62 is waiting at Starchild Numerology.Pickup a passenger going to Cyclone.Go to Cyclone:e 1 l 2 r.Pickup a passenger going to What's The Difference.Pickup a passenger going to Divide and Conquer.Pickup a passenger going to Divide and Conquer.Go to Divide and Conquer:n 2 r 2 r 1 r.Pickup a passenger going to Trunkers.Go to Trunkers:e 1 r 3 r 1 l.Pickup a passenger going to Multiplication Station.Go to Cyclone:w 2 r.Pickup a passenger going to Multiplication Station.Go to Multiplication Station:s 1 l 2 r 4 l.Pickup a passenger going to What's The Difference.Go to What's The Difference:n 2 l 1 r 3 l.Pickup a passenger going to Addition Alley.Go to Starchild Numerology:e 1 r 3 l 2 r.1 is waiting at Starchild Numerology.63 is waiting at Starchild Numerology.Pickup a passenger going to Addition Alley.Pickup a passenger going to The Underground.Go to Addition Alley:e 1 l 2 r 3 r 1 r.Pickup a passenger going to Joyless Park.Go to Writer's Depot:n 1 l 1 l.ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789- is waiting at Writer's Depot.Pickup a passenger going to Chop Suey.Go to Joyless Park:n 3 r 2 r 2 l.Go to Chop Suey:w 1 r 1 r 1 l.[b]Pickup a passenger going to Narrow Path Park.Go to Narrow Path Park:n 1 l 1 r 1 l.Go to The Underground:e 1 r.Switch to plan "c" if no one is waiting.Pickup a passenger going to The Underground.Go to Fueler Up:s.Go to Chop Suey:n 3 r 1 l.Switch to plan "b".[c]Go to Joyless Park:n 1 r.Pickup a passenger going to The Underground.Go to Narrow Path Park:w 1 r 3 l.[d]Pickup a passenger going to KonKat's.Go to KonKat's:e 1 r.Pickup a passenger going to KonKat's.Go to The Underground:s.Switch to plan "e" if no one is waiting.Pickup a passenger going to The Underground.Go to Fueler Up:s.Go to Narrow Path Park:n 4 l.Switch to plan "d".[e]Go to KonKat's:n.Pickup a passenger going to Riverview Bridge.Go to Riverview Bridge:n 1 l.Go to Narrow Path Park:e 1 l 1 r.Pickup a passenger going to Post Office.Go to Post Office:e 1 r 4 r 1 l.Go to Sunny Skies Park:s 1 r 1 l 1 r.Pickup a passenger going to The Underground.Go to The Underground:n 1 r 1 r 2 r.Switch to plan "f" if no one is waiting.Pickup a passenger going to Sunny Skies Park.Go to Sunny Skies Park:n 3 l 2 l 1 l.Switch to plan "a".[f]

Try it online!

Taxi is super not made for this but you can do it! I'll try to explain what's happening below the un-golfed version.

Go to Post Office: west 1st left 1st right 1st left.
Pickup a passenger going to The Babelfishery.
Go to The Babelfishery: south 1st left 1st right.
Pickup a passenger going to Sunny Skies Park.
Go to Sunny Skies Park: north 1st left 1st left 1st right.
[a]
Go to Heisenberg's: north 1st right 1st right 3rd right.
Pickup a passenger going to Cyclone.
Go to Go More: north 1st left 3rd left 3rd left.
Go to Starchild Numerology: east 2nd right.
62 is waiting at Starchild Numerology.
Pickup a passenger going to Cyclone.
Go to Cyclone: east 1st left 2nd right.
Pickup a passenger going to What's The Difference.
Pickup a passenger going to Divide and Conquer.
Pickup a passenger going to Divide and Conquer.
Go to Divide and Conquer: north 2nd right 2nd right 1st right.
Pickup a passenger going to Trunkers.
Go to Trunkers: east 1st right 3rd right 1st left.
Pickup a passenger going to Multiplication Station.
Go to Cyclone: west 2nd right.
Pickup a passenger going to Multiplication Station.
Go to Multiplication Station: south 1st left 2nd right 4th left.
Pickup a passenger going to What's The Difference.
Go to What's The Difference: north 2nd left 1st right 3rd left.
Pickup a passenger going to Addition Alley.
Go to Starchild Numerology: east 1st right 3rd left 2nd right.
1 is waiting at Starchild Numerology.
63 is waiting at Starchild Numerology.
Pickup a passenger going to Addition Alley.
Pickup a passenger going to The Underground.
Go to Addition Alley: east 1st left 2nd right 3rd right 1st right.
Pickup a passenger going to Joyless Park.
Go to Writer's Depot: north 1st left 1st left.
ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789- is waiting at Writer's Depot.
Pickup a passenger going to Chop Suey.
Go to Joyless Park: north 3rd right 2nd right 2nd left.
Go to Chop Suey: west 1st right 1st right 1st left.
[b]
Pickup a passenger going to Narrow Path Park.
Go to Narrow Path Park: north 1st left 1st right 1st left.
Go to The Underground: east 1st right.
Switch to plan "c" if no one is waiting.
Pickup a passenger going to The Underground.
Go to Fueler Up: south.
Go to Chop Suey: north 3rd right 1st left.
Switch to plan "b".
[c]
Go to Joyless Park: north 1st right.
Pickup a passenger going to The Underground.
Go to Narrow Path Park: west 1st right 3rd left.
[d]
Pickup a passenger going to KonKat's.
Go to KonKat's: east 1st right.
Pickup a passenger going to KonKat's.
Go to The Underground: south.
Switch to plan "e" if no one is waiting.
Pickup a passenger going to The Underground.
Go to Fueler Up: south.
Go to Narrow Path Park: north 4th left.
Switch to plan "d".
[e]
Go to KonKat's: north.
Pickup a passenger going to Riverview Bridge.
Go to Riverview Bridge: north 1st left.
Go to Narrow Path Park: east 1st left 1st right.
Pickup a passenger going to Post Office.
Go to Post Office: east 1st right 4th right 1st left.
Go to Sunny Skies Park: south 1st right 1st left 1st right.
Pickup a passenger going to The Underground.
Go to The Underground: north 1st right 1st right 2nd right.
Switch to plan "f" if no one is waiting.
Pickup a passenger going to Sunny Skies Park.
Go to Sunny Skies Park: north 3rd left 2nd left 1st left.
Switch to plan "a".
[f]

Start: Get stdin
Pick up the stdin value as text, convert it to a number, and go stick it somewhere to wait.

Plan A Part 1: Get a random integer 1-62
Get a random integer and then get 62 as a number. Duplicate both the random integer and the 62 because we'll need them later. You can only carry 3 passengers at once so we end up with rand, rand, and 62. (The other 62 will wait around until we get back.) Go divide rand by 62 and truncate the result to get an integer. Go back to get the other copy of 62 and multiply it by the truncated integer from the division. Finally, subtract the product from the first copy of rand. This gives us a number 0-61. Now we have to go back to pickup a 1 and add it to the result to get a number 1-62. Yes, all those many lines of text are just mod(rand(),62)+1.

Plan A Part 2: Create an array of characters from which to choose
Pickup a string with all the valid characters and also one at the end we don't want (more on that later). The 63 we picked up earlier matches this string length. Take it over to Chop Suey to have it broken into individual passengers.

Plan B: Move the array so we can select a character
One by one, move every character over to Narrow Path Park. It's the only stack available and the only way to not have leftover passengers getting in the way. Everything else in Townsburg is FIFO so I would have to go back and clear out all the passengers every iteration of the overall loop. This way, I can just leave them at the park and they'll get pushed out of the way by the 63 new characters every time. The very first A is likely to never escape.

Plan C: Prepare to select a character
This is really just a few stops that didn't need to be in Plan D. Re-position the taxi in preparation.

Plan D: Get all the characters we dont want
Starting with the first character in the reversed "array" (this is the 63rd character we don't want), keep picking up and concatenating characters as we count down from the result of the mod function in Plan A. Once you hit zero, the next character is the one you want.

Plan E: Drown the ones you don't want and return the chosen one.
"[P]assengers dropped off at Riverview Bridge seem to always fall over the side and into the river..." Well, that gets rid of that concatenated string of losers. Go pick up the next character and send it to stdout. Finally, let's check how many characters we've printed thus far. Back to Sunny Skies to pick up the stdin value we left so long ago. Subtract one and, if the result is more than zero, send it back to wait and start over again at Plan A.

Snowman, 58 bytes

((}#`""*:48vn58nR|65vn91nR,aC|97vn123nR,aCAsH1AaL#aC*;bR))

Try it online!

This is a subroutine that takes an integer as input and returns the random string.

((             subroutine
  }            make b, e, g active
  #`           e = input (from +)
  ""*          store an empty string in +
  :            what follows is the block to prepend a random char to +
    48vn58nR|  generate range(48..58) and place in g (need b and e for next step)
    65vn91nR   generate range(65..91) in b
    ,aC|       move g to e, concatenate b and e, and move the result to g
    97vn123nR  generate range(97..123) in b
    ,aC        move g to e, concatenate b and e, keeping the result in b
    AsH        shuffle the array of candidate ASCII codes stored in b
    1AaL       equivalent to 0aAwR - get the first element wrapped in an array
    #aC        retrieve + and prepend the randomly generated character
    *          store back into +
  ;bR          repeat this block e times, where e has been set to the input
))             output is given via +

Alice, 24 bytes

/w9u"Uz;r
\0.rdao"ki@/t&

Try it online!

This layout is already a lot better than what I originally had (32 bytes), but I'm sure it's not optimal yet...

Explanation

/      Reflect to SE. Switch to Ordinal.
       The IP now bounces diagonally up and down through the code.
09     Append 0 and 9 to an (implicit) empty string to create "09".
r      Range expansion, turns the string into "0123456789".
"az"   Push this string.
r      Range expansion, turns it into the lower-case alphabet.
i      Read all input as a string.
/      Reflect to E. Switch to Cardinal.
t      Implicitly convert the input string to the integer value N it
       contains and decrement it.
&      Run the next command N-1 times.
       The IP wraps around to the first column.
\      Reflect to NE. Switch to Ordinal. (This is not a command.)
w      Push the current IP address to the return address stack N-1
       times. This starts a loop whose body will run N times.
  .      Duplicate the lower-case alphabet.
  u      Convert it to upper case.
  d      Push the concatenation of all values on the stack. This pushes
         a single string with digits, lower-case and upper-case alphabet.
  U      Random choice. Pick a character from this string uniformly at random.
  o      Print it.
  ;      Discard the upper-case alphabet, because it will be regenerated
         in the next loop iteration (and if we leave it, then upper-case
         letters will become more and more likely as the output grows).
k      As long as there is still an address on the return address stack,
       jump back to that address (i.e. to the w). Once the return address
       stack has been depleted, this does nothing and the loop is exited.
@      Terminate the program.

C (gcc), 57 55 52 bytes

Thanks to 2501 for the pointers...

i;f(n){for(;n-=isalnum(i=rand()%150)&&putchar(i););}

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JavaScript (ES6), 61 54 39 52 64 bytes

This is almost like reverse-golf! Took a big hit on the byte count ensuring that the full range of characters from all three groups would be used.

f=n=>n--?btoa(String.fromCharCode(Math.random()*248))[0]+f(n):""

• 15 bytes saved (at one stage) thanks to Arnauld's suggestion of using a recursive function.

Try it

f=n=>n--?btoa(String.fromCharCode(Math.random()*248))[0]+f(n):""
i.addEventListener("input",_=>o.innerText=f(+i.value))

<input id=i type=number><pre id=o>

Python 3, 132 124 123 bytes

...I most probably can golf this further. Might be able to do that by using ASCII numbers. Tried and ended up longer than Java.

from random import*
a='abcdefghijklmnopqrstuvwxyz0123456789'
f=lambda n:''.join(choice(a+a[:-10].upper())for i in range(n))

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R, 54 52 51 49 bytes

intToUtf8(sample(c(65:90,97:122,48:57),scan(),T))

Explanation:

1. Read input integer n: scan()
2. Vector with ASCII values: c(65:90,97:122,48:57)
3. Sample n ASCII values with replacement: sample(c(65:90,97:122,48:57),scan(),T)
4. Transform ASCII values to a character string with intToUtf8

R, 51 bytes

Same length as the other R answer, but a different approach.

cat(sample(c(letters,LETTERS,0:9),scan(),T),sep="")

letters and LETTERS both are built-in variables containing all lower and uppercase letters respectively. Adding 0:9 to that and we have the entire set of alphanumeric characters.

MATL, 8 bytes

8Y2iT&Zr

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8Y2      % Push string '012...89ABC...YZabc...yz'
i        % Input N
T&Zr     % Sample with replacement. Implicitly display

Brachylog, 14 bytes

~l{Ạụ:Ạ:Ịcṛ}ᵐc

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Explanation

~l                 Create a list of length Input
  {        }ᵐ      Map on each element of that list:
   Ạụ:Ạ:Ịc           The string "A…Za…z0…9"
          ṛ          Pick a character at random
             c     Concatenate into a single string

Stacked, 33 bytes

:>[alpha 10:>ALPHA,,''#`randin]"!

Try it online! Takes input from the top of the stack and leaves output on the top of the stack.

:>[alpha 10:>ALPHA,,''#`randin]"!
:>                                  range from 0 to n-1
  [                           ]"!   on each, do:
   alpha                            push "abc...xyz"
         10:>                       push (0 1 2 ... 8 9)
             ALPHA                  push "ABC...XYZ"
                  ,,                concat twice
                    ''#`            join by nothing
                        randin      select random member in it

C, 60 bytes

r;f(n){for(;n--;)r=rand()%62,putchar(r+=r>9?r>35?61:55:48);}

See it work here.

See the distribution here.

It is uniformly distributed, assuming rand() % 62 produces a uniform distribution. Since 62 usually doesn't evenly divide RAND_MAX, there is a very small bias.

Shell + pwgen, 13 bytes

pwgen -s $1 1

-s, --secure

Generate completely random, hard-to-memorize passwords.

Sample output

%pwgen -s 10 1
2cyhLovbfT

Perl 5, 41 bytes

40 bytes of code + -p flag.

$\.=(a..z,A..Z,0..9)[rand 62]for 1..$_}{

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(a..z,A..Z,0..9) creates an array containing all letters and numbers, [rand 62] returns an random element of this array, which is append (.=) to $\, which is implicitly printed at the end thanks to -p flag with }{.

Or, for the same bytecount, but using the parameters rather than the standart input:

print+(a..z,A..Z,0..9)[rand 62]for 1..pop

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05AB1E, 6 bytes

FžK.RJ

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Explanation

F        # input number of times do
 žK      # push [a-zA-Z0-9]
   .R    # pick one at random
     J   # join to string