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

(a) $\frac{9!}{(2!{)}^3}$
The word COMMITTEE consists of 9 letters including two Ts, two Ms and two Es.
Number of words that can be formed = Number of arrangements of 9 things taking all at a time, of which 2 are similar of the first kind, 2 are similar of the second kind and 2 are similar of the third kind = $\frac{9!}{2!2!2!}=\frac{9!}{(2!{)}^3}$