Question

Write the number of words can be formed out of the letters of the word 'COMMITTEE'.

Answer 1

There are 9 letters in the word 'COMMITTEE' out of which 2 are M's, 2 are T's 2 are E's and the rest are all distinct.

$\therefore$ The required number of words

=$\frac{9!}{2!2!2!}=\frac{9!}{(2!{)}^3}$

Hence, the total number of words are $\frac{9!}{(2!{)}^3}$