Finding the number of ways to arrange identical balls in a circle

[songoku]

Homework Statement

Find the number of ways to arrange 2 red balls, 2 blue balls and 1 yellow ball in a circle

Relevant Equations

cyclic permutation = (n - 1)!

permutation with identical objects = $\frac{n!}{r_{1}! r_{2}! ...}$

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got $\frac{(4-1)!}{2!2!}=\frac{3}{2}$ which does not make sense.

Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities?

Thanks

 

[PeroK]

I assume that two arrangements are considered equal if they are equal after rotation?

If so, you could start by fixing the position of the yellow ball.

 

[BvU]

$\frac{(4-1)!}{2!2!}=\frac{3}{2}$ which does not make sense.

Why 4 ?