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 :-
|
a. |
(15)! × 6! |
b. |
56 × 15 |
|
c. |
5! × 6! |
d. |
65 × (15)! |
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 :-
|
a. |
(15)! × 6! |
b. |
56 × 15 |
|
c. |
5! × 6! |
d. |
65 × (15)! |
f(k) = 3m (3,6,9,12,15,18)
for k = 4,8,12,16,20 6.5.4.3.2 ways
For rest numbers 15! ways
Total ways = 6!(15!)