# 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:Option 1)$(15)! \times 6!$Option 2)$5! \times 6!$Option 3)$6^{5}\times(15)!$Option 4)$5^{6} \times 15$

Onto function -

If  f:A$\rightarrow$B is such that each & every element in B is the f image of atleast 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!

Option 1)

$(15)! \times 6!$

Option 2)

$5! \times 6!$

Option 3)

$6^{5}\times(15)!$

Option 4)

$5^{6} \times 15$

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