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:

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: Correct Answer (15)! × 6!

From question,

F = {1, 2, 3,…,20}

f(x) ∈ {3, 6, 9, 12, 15, 18}

k ∈ {4, 8, 12, 16, 20}

From question, we need to assign the value of f(k) for k ∈ {4, 8, 12, 16, 20} which is:

⇒ ⁶C₅ .5!

⇒ 6 × 5!

⇒ 6!

Now, apart from ‘k’ being multiplies of 4. There are 15 elements left in the given function.

Rest of the elements are associated with the another set in 15! Ways.

Total number of onto functions are: