Since we know, Permutation of n objects taking r at a time is ⁿP_r,and permutation of n objects taking all at a time is n!

And, we also know Permutation of n objects taking all at a time having p objects of the same type, q objects of another type, r objects of another type is . i.e. the, number of repeated objects of same type are in denominator multiplication with factorial.

Given, the word EXERCISES. It has 9 letters, and it has 2 repeated letters ‘E’, and ‘S.’ The letter E is repeated thrice, and letter S is repeated twice. And all other letters are distinct.

The problem can now be rephrased as to find total number of permutations of 9 objects (E, X, E, R, C, I, S, E, S) of which three objects are of same type (E, E, E), and two objects are of another type (S, S).

Total number of such permutations

= 30240

Hence, a total number of permutations of the word EXERCISES is 30240.