The Mississipi counting problem, this time in circle

Question

I have another version of the Mississippi problem.
How many ways we can arrange the letters, if we put them in a circle:
Mississippi and Ississippim - are the same.
I can't find a practical way to solve it. any suggestions?

Answer 1

M is an only unique element. So, seat M first.
This breaks the symmetry of a round table, and remaining seats just act as a straight line.

So, you have to seat $$i,i,i,i,s,s,s,s,p,p$$ i.e. 10 elements in a row. Do this in: $$\frac{10!}{4!\cdot4!\cdot2!}$$ This is the total number of arrangements.