# Math Help - Permutation Question

1. ## Permutation Question

Hello,
My question is :How many words can be formed by using the letters of "MARMARA"? And if you provide a proof for the formula that is used I would be grateful. Thanks for help.

2. Originally Posted by JohnDoe
Hello,
My question is :How many words can be formed by using the letters of "MARMARA"? And if you provide a proof for the formula that is used I would be grateful. Thanks for help.
The number of words can be formed by using the letters of "MISSISSIPPI" is $\frac{11!}{(4!)^2(2!)}$.

3. I think the answer would be
$

\frac{7!}{(2!)^2(3!)}
$
But why there is a formula like this I would like to know why we divide it by that factorial etc. Can anyone provide me that information?

4. Originally Posted by JohnDoe
I think the answer would be
$\frac{7!}{(2!)^2(3!)}
$
But why there is a formula like this I would like to know why we divide it by that factorial etc. Can anyone provide me that information?
Consider the word "UNUSUAL", and ask the same question.
If we put subscripts on the U's $U_1 NU_2 SU_3 AL$ now we have seven different letters and the answer would be $7!$.
But the string $U_1 U_2 U_3$ can be rearranged is $3!$ ways.
So removing the subscripts makes us divide by that: $\frac{7!}{3!}$.

5. Much thanks but I still think I did not get the meaning exactly. If you explain all the steps maybe I can understand. Why don't we group all the U s together than say the number of elements are 5 then continue our work. It does not matter if it is the U number one getting the first place or U number two getting the first place there is no difference. So IMO we should eliminate these opinions but how I just can not figure it out and trial method is way too long even for attempting. Is there any place where I can find the proof on the net?

6. Originally Posted by JohnDoe
explain all the steps
There are no steps! It is just a matter of thinking about it.
We must divide to account for repeated letters.