Problem Solving

In how many ways can be 6 boys and 6 girls sit around circular table so that no two boys sit next to each other?

A)(5!)^2
B)(6!)^2
C)5!6!
D)11!
E)(5!)^2 6!

I got (6!)^2 but the OA C

j_shreyans wrote:In how many ways can be 6 boys and 6 girls sit around circular table so that no two boys sit next to each other?

A)(5!)^2
B)(6!)^2
C)5!6!
D)11!
E)(5!)^2 6!

I got (6!)^2 but the OA C

For arrangements around a circular table:

1. First seat someone at the table.
2. Then count the number of ways to arrange the OTHER people relative to the first person.

In the problem above, no two boys can sit in adjacent seats.
Implication:
Boys and girls must ALTERNATE around the table.

Let the 12 seats be A, B, C, D, E, F, G, H, I, J, K, L.
Let a boy sit at seat A.
The remaining 5 boys must occupy seats C, E, G, I, and K.
The number of ways to arrange the remaining 5 boys in these 5 seats = 5!.
The 6 girls must occupy the remaining 6 seats.
The number of ways to arrange the 6 girls in these 6 seats = 6!.
To combine the options above, we multiply:
5!6!.

The correct answer is C.