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 \(\frac{n!}{p!\times q!\times r!}\).
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 = \(\frac{5!}{2!}\)
= 60
Hence,
A total number of permutations of the word INDIA is 60.
