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 si

Monjur Alahi

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!`


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Salim Ahmed Kawsar

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Correct Answer - 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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