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Number of permutations of 1,2,3,4,5,6,7,...

Number of permutations of `1,2,3,4,5,6,7,8`, and `9` taken all at a time are such that digit `1` appearing somewhere to the left of `2` and digit `3` appearing to the left of `4` and digit `5` somewhere to the left of `6`, is
(e.g. `815723946` would be one such permutation)

A

`9.7!`

B

`8!`

C

`5!4!`

D

`8!4!`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` Number of digits are `9`
Select `2` places for the digit `1` and `2` in `"^(9)C_(2)` ways from the remaining `7` places, select any two places for `3` and `4` in `"^(7)C_(2)` ways and from the remaining `5` places select any two for `5` and `6` in `"^(5)C_(2)` ways.
`:.` Total ways `="^(9)C_(2)*^(7)C_(2)*^(5)C_(2)*3!`
`=(9!)/(2!7!)*(7!)/(2!5!)*(5!)/(2!3!)*3!`
`=(9!)/(8)=(9*8*7!)/(8)=9*7!`
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