Q. 214.5( 4 Votes )

Find the total number of permutations of the letters of the word ‘INSTITUTE’.

Answer :

Given, the word INSTITUTE. It has 9 letters and it has 2 repeated letters ‘I’ and ‘T’. The letter I is repeated twice, and letter T is repeated thrice. And all other letters are distinct.

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

Since we know, Permutation of n objects taking r at a time is nPr,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 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.

Total number of such permutations

= 30240

Hence, total number of permutations of the word INSTITUTE is 30240.

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