How many distinguishable words can be formed from the letters of the word "casserole" if each letter is used exactly once? answer is 90,720

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- Dec 23rd 2010, 12:09 PMbigwavehow many distinguishable words
How many distinguishable words can be formed from the letters of the word "casserole" if each letter is used exactly once? answer is 90,720

- Dec 23rd 2010, 12:16 PMPlato
If the same question were asked about the word $\displaystyle MISSISSIPPI$ then the answer is $\displaystyle \dfrac{11!}{4!\cdot 4!\cdot 2!}$.

Study that and apply to your question. - Dec 23rd 2010, 12:35 PMjanvdl
- Dec 23rd 2010, 12:38 PMbigwave
thanks that was it

- Dec 23rd 2010, 08:46 PMbigwaveCasserole
so then

there are 9 letters in the word.

(2) s (2) e

$\displaystyle \frac{9!}{2!2!} \rightarrow \frac{362880}{4} = 90720$