he number of functions f from {1, 2, . . . , 20} onto {1, 2, . . . , 20} such that f(k) is a multiple of 3whenever k is a multiple of 4 is(a) 5! · 6! · 9!(b) 5^6· 15!(c) 6^5· 14!(d) 15! · 6!

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