"The number of k-permutations is always less (or equal) than the numer of k-tupels", is a known simple truth in combinatorics:
Table[n!/(n - k)! <= n^k, {n, 1, 100}, {k, 1, n}] (* Out= {True,True,True,etc} *)
I've tried combinations of Simplify, FullSimplify, Reduce, FunctionExpand, Assuming, Assumptions and can't get a True (i actually once got a False). A failing example with Reduce is:
Reduce[n!/(n - k)! <= n^k && n > k && k > 0, {n, k}, Integers]
Does anyone have better luck in getting a True for this inequality expression?