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  4. 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 :

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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 :

JEE MainJEE Main 2019Relations and Functions - Part 2

Solution:

$f(k) = 3m (3,6,9,12,15,18)$
for $k = 4,8,12,16,20 6.5.4.3.2$ ways
For rest numbers $15!$ ways
Total ways = $6!(15!)$