algorithm - Complexity when generating all combinations -

interview questions start "this might solved generating possible combinations array elements" meant let me find better.

anyway add "i prefer solution since o(x)".. question is: o(x) complexity of generating combinations given set?

i know there n! / (n-k)!k! combinations (binomial coefficients), how big-o notation that?

first, there nothing wrong using o(n! / (n-k)!k!) - or other function f(n) o(f(n)), believe looking simpler solution still holds same set.

if willing @ size of subset k constant,

for k<=n-k:

n! / ((n-k)!k!) = ((n-k+1) (n-k+2) (n-k+3) ... n ) / k!  

but above (n^k + o(n^(k-1))) / k!, in o(n^k)

similarly, if n-k<k, o(n^(n-k))

which gives o(n^min{k,n-k})