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Three boys and two girls stand in a queu...

Three boys and two girls stand in a queue. The probability, that the number of boys ahead is at least one more than the number of girls ahead of her is?

A

`(1)/(2)`

B

`(1)/(3)`

C

`(2)/(3)`

D

`(3)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
3 Boys and 2 Girls …
(1) B (2) B (3) B (4)
Girl can't occupy 4th position.
Either girls can occupy 2 of 1, 2, 3 position or they can both be at position (1) or (2).
Hence, total number of ways in which girls can be seated
`=.^(3)C_(2) xx 2! xx 3! + .^(2)C_(1) xx 2! xx 3! = 36 + 24 = 60`.
Number of ways in which 3 boys and 2 girls can be seated = 5!
`therefore` Required probability = `(60)/(5!) = (1)/(2)`
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