Question

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

• A. $\left(15\right)!\times 6!$
• B. $5^6\times 15$
• C. $5!\times 6!$
• D. $6^5\times \left(15\right)!$

Answer 1

Answer: (A)

$\left(15\right)!\times 6!$

$f\left(x\right)=3m(3,6,9,12,15,18)$
for $k=4,8,12,16,20\mathrm{6.5.4.3.2}$ ways
For rest numbers $15!$ ways
Total ways =$6!(15!)$