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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?
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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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