# Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.

Question:

Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.

Solution:

The word 'MATHEMATICS' consists of 11 letters including two Ms, two Ts and two As

Number of words that can be formed out of the letters of the word MATHEMATICS = Number of arrangements of 11 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 $=\frac{11 !}{2 ! 2 ! 2 !}$