# how many distinguishable words

• Dec 23rd 2010, 01:09 PM
bigwave
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
• Dec 23rd 2010, 01:16 PM
Plato
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.
• Dec 23rd 2010, 01:35 PM
janvdl
Quote:

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.
• Dec 23rd 2010, 01:38 PM
bigwave
thanks that was it
• Dec 23rd 2010, 09:46 PM
bigwave
Casserole
so then

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

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