Question:
The number of functions $\mathrm{f}$ from $\{1,2,3, \ldots, 20\}$ onto $\{1,2,3, \ldots \ldots, 20\}$ such that $f(k)$ is a multiple of 3 , whenever $\mathrm{k}$ is a multiple of 4 , is :-
Correct Option: 1
Solution:
$f(\mathrm{k})=3 \mathrm{~m}(3,6,9,12,15,18)$
for $k=4,8,12,16,20$ $6.5 .4 .3 .2$ ways
For rest numbers 15 ! ways
Total ways $=6 !(15 !)$
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