Q. 1 E

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

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 PAKISTAN. It has 8 letters, and it has 1 repeated letter ‘A.’ The letter A is repeated twice, and all other letters are distinct.

The problem can now be rephrased as to find a total number of permutations of 8 objects (P, A, K, I, S, T, A, N) of which two objects are of same type (A, A).

Total number of such permutations

= 20160

Hence, a total number of permutations of the word PAKISTAN is 20160.

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