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  • number of functions f from{1,2,3...,20}onto{1,2,3...,20} such that f(k) is mulitiple of 3, where k is multiple of 4

number of functions f from{1,2,3...,20}onto{1,2,3...,20} such that f(k) is mulitiple of 3, where k is multiple of 4

Answers (1)

Onto function -

If f: A\rightarrowB is such that each & every element in B is the f image of at least one element in A.Then it is Onto function.

- wherein

The range of f is equal to Co - domain of f.

f(k) = 3,6,9,12,15,18

for k = 4,8,12,16,20

ways = 6 x 5 x 4 x 3 x 2 x 1 = 6!

For remaining numbers = (20-5)! = 15!

Total ways = 15! x 6!

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