First slide

Permutations

Question

If all permutations of the letters of the word AGAIN are arranged as in dictionary, the forty-ninth word is

Moderate

A

NAAGI
B

NAGAI
C

NAAIG
D

NAIAG

Solution

Starting with the 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 $\frac{4!}{2! 1! 1!} = 12$ words, the 37th word starts with I and there are 12 words starting with I. Total goes up to 48 words.
Now, 49th word is NAAGI.

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