# perms and combs circle qn (1 Viewer)

#### Masaken

##### Member
Four boys and four girls are arranged in a circle. In how many ways can this be done, if the boys and the girls are in distinct groups?

Would it be 4! x 4! (because you only need to mix around the boys and girls separately) or 3! x 4! (fix one boy first) ? I've received conflicting answers on this.

#### cossine

##### Active Member
Four boys and four girls are arranged in a circle. In how many ways can this be done, if the boys and the girls are in distinct groups?

Would it be 4! x 4! (because you only need to mix around the boys and girls separately) or 3! x 4! (fix one boy first) ? I've received conflicting answers on this.
So if they are in distinct groups as in two different circle then you would get:

3! * 3! due to rule of product axiom.

#### 5uckerberg

##### Well-Known Member
Four boys and four girls are arranged in a circle. In how many ways can this be done, if the boys and the girls are in distinct groups?

Would it be 4! x 4! (because you only need to mix around the boys and girls separately) or 3! x 4! (fix one boy first) ? I've received conflicting answers on this.
Considering your answer @Masaken it would be $\bg_white 2\left(3!\times{4!}\right)$ if the boys and girls are sitting at the same table but because this question is about distinct groups you are basically separating the boys and girls and you will get the answer that @cossine wrote because of this reason.