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.
Consider the word "UNUSUAL", and ask the same question.
If we put subscripts on the U's $\displaystyle U_1 NU_2 SU_3 AL $ now we have seven different letters and the answer would be $\displaystyle 7!$.
But the string $\displaystyle U_1 U_2 U_3 $ can be rearranged is $\displaystyle 3!$ ways.
So removing the subscripts makes us divide by that: $\displaystyle \frac{7!}{3!}$.
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?