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  4. If all permutations of the letters of the word AGAIN are arranged as in dictionary, then fiftieth word is

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Q. If all permutations of the letters of the word AGAIN are arranged as in dictionary, then fiftieth word is

Permutations and Combinations

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.
Hence, total 36 words.
Next, the 37th word starts with I. There are 12 words starting with I. This accounts up to the 48th word. The 49th word is NAAGI. The 50th word is NAAIG.