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 :

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 : (A) (15)! × 6! (B) 56 × 15 (C) 5! × 6! (D) 65 × (15)!

Tardigrade Admin · Accepted Answer

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!)

Q. 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 :

$(15)! \times 6!$

$5^{6} \times 15$

$5! \times 6!$

$6^{5} \times (15)!$

$f (k) = 3 m (3, 6, 9, 12, 15, 18)$
for $k = 4, 8, 12, 16, 206.5.4.3.2$ ways
For rest numbers $15!$ ways
Total ways = $6! (15!)$

Q. 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 :

(15)!×6!

56×15

5!×6!

65×(15)!