Here are a few possibilities that don't parse the output of ls and that are 100% safe regarding files with spaces and funny symbols in their name. All of them will populate an array randf with a list of random files. This array is easily printed with printf '%s\n' "${randf[@]}" if needed.
This one will possibly output the same file several times, and N needs to be known in advance. Here I chose N=42.
a=( * )
randf=( "${a[RANDOM%${#a[@]}]"{1..42}"}" )
This feature is not very well documented.
If N is not known in advance, but you really liked the previous possibility, you can use eval. But it's evil, and you must really make sure that N doesn't come directly from user input without being thoroughly checked!
N=42
a=( * )
eval randf=( \"\${a[RANDOM%\${#a[@]}]\"\{1..$N\}\"}\" )
I personally dislike eval and hence this answer!
The same using a more straightforward method (a loop):
N=42
a=( * )
randf=()
for((i=0;i<N;++i)); do
randf+=( "${a[RANDOM%${#a[@]}]}" )
done
If you don't want to possibly have several times the same file:
N=42
a=( * )
randf=()
for((i=0;i<N && ${#a[@]};++i)); do
((j=RANDOM%${#a[@]}))
randf+=( "${a[j]}" )
a=( "${a[@]:0:j}" "${a[@]:j+1}" )
done
Note. This is a late answer to an old post, but the accepted answer links to an external page that shows terrible bash practice, and the other answer is not much better as it also parses the output of ls. A comment to the accepted answer points to an excellent answer by Lhunath which obviously shows good practice, but doesn't exactly answer the OP.