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Five boys and four girls sit in a row ra...

Five boys and four girls sit in a row randomly. The probability that no two girls sit together

A

`5/42`

B

`(1)/(8)`

C

`(7)/(40)`

D

`(1)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
A
Total number of cases = `5!`
Since `S_(1)` gets seat `R_(1)` and none of the other gets previously allotted seat, we have derangement of 4 students. So, required probability
`=(4!(1-(1)/(1!)+(1)/(2!)-(1)/(3!)+(1)/(4!)))/(5!) = (9)/(120) = (3)/(40)`
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