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

The correct option is A $\frac{9!}{(2!{)}^3}$

There are 9 letters in the given word in which two T's, two M's and two E's are identical. Hence the required number of words $=\frac{9!}{2!2!2!}=\frac{9!}{(2!{)}^3}$