Circular table permutations problem

Hey, i have problem understanding how to get result for circular permutations where i have repeating elements.

I have 10 people in circle, 3 man and 7 women. How can i get number of permutations?

Result in book is 36.

I tried

(9!/2!+7!)+(9!/3!+6!)=120 which is wrong.

Re: Circular table permutations problem

Quote:

Originally Posted by

**PJani** Hey, i have problem understanding how to get result for circular permutations where i have repeating elements. I have 10 people in circle, 3 man and 7 women. How can i get number of permutations?

**Result in book is 36.**

That problem as you have posted it is **absolutely **__incomplete__.

As stated the answer is simply $\displaystyle 9!$.

There must be many more conditions placed on the groups of men and women.

Please add in those further conditions. That is the only way the answer $\displaystyle 36$ makes any sense.

Re: Circular table permutations problem

Heh sory, my mistake!

How can i get number of permutations where i distinguish persons only by gender?

Re: Circular table permutations problem

Quote:

Originally Posted by

**PJani** Heh sory, my mistake!

How can i get number of permutations where i distinguish persons only by gender?

In the future, please try to be clear and complete.

Place a female anywhere at the table.

Now you have a string $\displaystyle ffmmmmmmm$ to arrange: $\displaystyle \frac{9!}{2!\cdot 7!}=?$ ways.

Start at the seated female's right and seat each of those strings counter-clockwise.

Re: Circular table permutations problem

Why do you start with females? And why is $\displaystyle \frac{9!}{2!\cdot 7!}=?$ and not $\displaystyle \frac{9!}{3!\cdot 6!}=?$