# Find the total number of permutations of the letters of the word 'INSTITUTE'.

Question:

Find the total number of permutations of the letters of the word 'INSTITUTE'.

Solution:

The word 'INSTITUTE' consists of 9 letters including two Is and three Ts.

Total number of words that can be formed of the word INSTITUTE = Number of arrangements of 9 things of which 2 are similar to the first kind and 3 are similar to the second kind $=\frac{9 !}{2 ! 3 !}$