Question

The number of functions f from {1,2,...,20} into {1,2,....,20} such that f(k) is a multiple of 3 whenever k is a multiple of 4 is

Answer 1

there are 5 elements which are multiple of 4 .            There are 6 elements which are multiple of 3 .

so the elements which are multiple of 4 are only mapped to one in  the elements which are multiple of 3.

for remaining 15 elements we can map to any one of 20 elements.

   6⁵ * 20¹⁵