# Math Help - how many distinguishable words

1. ## how 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

2. If the same question were asked about the word $MISSISSIPPI$ then the answer is $\dfrac{11!}{4!\cdot 4!\cdot 2!}$.

Study that and apply to your question.

3. Originally Posted by bigwave
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
To add on to Plato's example, notice that you take the factorial of the number of letters and divide it by the factorials of the number of times a letter is repeated.

4. thanks that was it

5. ## Casserole

so then

there are 9 letters in the word.
(2) s (2) e

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