SOLUTION: How many distinct permutations can be made out of the word "CONCOCTION" that begins and ends with letter "C"?

Question 847245: How many distinct permutations can be made out of the word "CONCOCTION" that begins and ends with letter "C"?
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
Fix the first and last letters to be C.
How many different letters can the 2nd spot be? 8
3rd? 7
4th? 6
5th? 5
etc.
9th? 1
We have 8! ways to arrange, but we need to factor out the order to get distinctness.
There are 3 Os, 2 Ns, 1 C, 1 T and 1 I. We really only need to concern ourselves with these multiple letters (O and N)
There is 3! ways to order the Os.
There is 2! ways to order the Ns.
So our total distinct permutations is 8! / (3! * 2!) [which is a variation of our multinomial formula]. This gives us 3360.

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