Write the number of words that can be formed out of the letters of the word ‘COMMITTEE’.
Question:

Write the number of words that can be formed out of the letters of the word ‘COMMITTEE’.

Solution:

The word COMMITTEE consists of 9 letters including two Ms, two Ts and two Es.

Number of words that can be formed out of the letters of the word COMMITTEE

= Number of arrangements of 9 things of which 2 are similar to the first kind,

2 are similar to the second kind and 2 are similar to the third kind $=\frac{9 !}{2 ! 2 ! 2 !}=\frac{9 !}{(2 !)^{3}}$