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The number of increasing function from f...

The number of increasing function from `f : AtoB` where `A in {a_(1),a_(2),a_(3),a_(4),a_(5),a_(6)}`, `B in {1,2,3,….,9}` such that `a_(i+1) gt a_(i) AA I in N` and `a_(i) ne i` is (a) `30` (b) `28` (c) `24` (d) `42`

A

`30`

B

`28`

C

`24`

D

`42`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` If `a_(1)` is mapped with `2`, we have `.^(7)C_(5)` ways of mapping rest of the elements.
If `a_(1)` is mapped with `3`, we have `.^(6)C_(5)` ways of mapping rest of the elelments.
If `a_(1)` is mapped with `4`, we have `.^(5)C_(5)` ways of mapping rest of the elements.
Hence total number of increasing function
`=^(7)C_(5)+^(6)C_(5)+^(5)C_(5)=28`
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