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The number of ways in which six boys and...

The number of ways in which six boys and six girls can be seated at a round table so that no two girls sit together and two particular girls do not sit next to a particular boy is

A

`6!4!`

B

`2.5!4!`

C

`2.6!4!`

D

`5!4!`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` The boys can be seated in `5!` ways.
If the girls `g_(1)` and `g_(2)` do not want to sit by the side of `A_(1)` (say).
The two gaps `A_(6)-A_(1)` and `A_(1)-A_(2)` must be filled by two of the remaining in `"^(4)P_(2)` ways.
The other four gaps can be filled in `4!` ways .
Hence the number of ways `=5!xx"^(4)P_(2)xx4!`
`=5!xx(4!)/(2!)xx4!`
`=2.6!4!`
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