Combinatorics question See attached image Prove that for all

Combinatorics question. See attached image.

Prove that for all positive integers n > k, the inequality k^n

Solution

number of ways to select n people form kn people is knCn...............(1)

lets divide the nk people in n sets of k people each,

number of ways to select n people with one from each set is k^n.........(2)

number of ways in (2) is obviously less than (1) , i.e

k^n < knCn

thus proved