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If set A={1, 2, 3,...20 }, then the find...

If set `A={1, 2, 3,...20 }`, 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

`(15)! xx 6!`

B

`5^(6) xx 15`

C

`5! xx6!`

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
According to when information, we have if
`k in {4,8,12,16,20}`
Then, `f(k) in {3, 6,9,12,15,18}`
`[ because " Codomain "(f)={1,2,3, …, 20}]`
Now, we need to assign the value of f(k) for
`k in {4,8,12,16,20}` this can be done in ` ""^(6)C_(5)*5! " ways " =6.5! =6!` and remaining 15 element can be associated by 15! ways.
`therefore "Total number of onto functions "=15!6!`
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