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If set A={1, 2, 3, ?2, }, then the find ...

If set `A={1, 2, 3, ?2, }`, then the find the number of onto functions from `A` to `A` such that `f(k)` is a multiple of 3, whenever `k` is a multiple of 4. (A) `6^5xx15!` (B) `5^6xx15!` (C) `6!xx5!` (D) `6!xx15!`

A

`6 ^(5) xx (15)!`

B

`(15)!xx6!`

C

`5!xx6!`

D

`5 ^(6) xx15`

Text Solution

Verified by Experts

The correct Answer is:
B
When `k =4,8,12,16,20`
Then `f (k)=3,6,9,12,15,18" " therefore` Total number of function `=(""^(6)C _(5) xx5!) xx15! = 6!xx15!`
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