Math Help - Circular Permutation??

1. Circular Permutation??

if there are 7 boys and 5 girls, how many circular arrangements are possible if the ladies do not sit adjacent to each other.??

2. Seat the boys at the table.
That can be done in $6!$ ways. WHY?
That creates seven places to place five chairs.
So what do you think the answer is?

3. Originally Posted by Plato
Seat the boys at the table.
That can be done in $6!$ ways. WHY?
That creates seven places to place five chairs.
So what do you think the answer is?
i think:-

=6!*p(7,5)
=6!*7!/(7-5)!

???

Tell us what those numbers mean!

5. Originally Posted by Plato

Tell us what those numbers mean!
boys ways;-(7-1)=6!
now there are 5 girls and 7 seats(in b/w boys) so there are P(7,5) number of ways, the girls can sit.
p(7,5)=7!/(7-5)!

i.e, total no. of ways= 6!*p(7,5)
= 6!*7!/(7-5)!
= 1814400 (but this ans is wrong).
ans is = 252

6. Originally Posted by Plato
7. Is it more than a coincidence that $\frac{15120}{60} = 252$?