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

Options

A. `6!4!`
B. `2.5!4!`
C. `2.6!4!`
D. `5!4!`

Answer

C

Explanation

`(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!`