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Find the number of words formed by permuting all the letters of the following words :

INDIA

Answer :

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 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 INDIA. It has 5 letters, and it has 1 repeated letter ‘I.’ The letter I is repeated twice and all other letters are distinct.


The problem can now be rephrased as to find a total number of permutations of 5 objects (I, N, D, I, A) of which two objects are of same type (I, I).


Total number of such permutations



= 60


Hence, a total number of permutations of the word INDIA is 60.


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