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If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?

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Question

If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?

Sum
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Solution

n Starting with letter A, and arranging the other four letters, there are 4! = 24 words.

These are the first 24 words.

Then starting with G, and arranging A, A, I and N in different ways

There are `(4!)/(2!1!1!)` = 12 words.

Next the 37th word starts with I.

There are again 12 words starting with I.

This accounts up to the 48th word.

The 49th word is NAAGI.

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Chapter 7: Permutations and Combinations - Solved Examples [Page 117]

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NCERT Exemplar Mathematics [English] Class 11
Chapter 7 Permutations and Combinations
Solved Examples | Q 5 | Page 117

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