Question

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

(1) 65 x (15)!

(2) 5! x 6!

(3) 56x 15

(4) (15)! x 6!

Answer 1

Correct option (4) (15)! × 6!

Explanation:

f(k) = (3, 6, 9, 12, 15, 18)

For k = 4, 8, 12, 16, 20

For these k we have 6.5.4, 3.2 ways = 6!

For other numbers we have 15! ways.

So total = 15!.6!