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Previous Year Question (PYQs)



The number of words with or without meaning which can be made using all the letters of the word AGAIN. If these words are written as in a dictionary, then the $50$th word will be





Solution

Letters: A, A, G, I, N Words starting with A: $ \frac{4!}{2!}=12 $ Starting with G: $ \frac{4!}{2!}=12 $ Starting with I: $ \frac{4!}{2!}=12 $ Total till I: $12+12+12=36$ Next start with N Remaining: A, A, G, I Arrangements: $ \frac{4!}{2!}=12 $ So positions $37$ to $48$ $49^{th}$ word = NAAGI $50^{th}$ word = NAAIG


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