Question

The number of words that can be formed out of the letters of the word "COMMITTEE" is

• A. $\frac{9!}{(2!{)}^3}$
• B. $\frac{9!}{(2!{)}^2}$
• C. $\frac{9!}{2!}$
• D. $9!$

Answer 1

Answer: (A)

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

The number of words that can be formed out of the letters of the word 'COMMITTEE' is equal to the number of permutation of the letters of the word

The word contains $9$ letters and among them there are $2$ Ms, $2$ Ts, $2$ Es,. That is repeatation occur $3$ times for three letters.

So, total number of words that can be formed is $=\frac{9!}{2!\times 2!\times 2!}=\frac{9!}{(2!{)}^3}$.