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

The correct option is D (15)!×6!
Domain ={1,2,3,4,...,20}
Co-domain ={1,2,3,4,...,20}
k={4,8,12,16,20}
f(k)={3,6,9,12,15,18}

Number of ways to arrange f(k) for k
=6×5×4×3×2=6!

Number of ways to arrange f(k) for remaining numbers =(205)!=15!
Total number of functions =6!×15!

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