JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

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

    A) NAAGI

    B) NAGAI

    C) NAAIG

    D) NAIAG

    Correct Answer: C

    Solution :

    [c] Starting with the letter A, and arranging the other four letters, there are 4! =24 words, these are the first 24 words. These are the first 24 words. Then stating with G, and arranging A, A, I, and N in different ways, there are \[\frac{4!}{2!1!1!}=\frac{24}{2}=12\] 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 words. The 49th word is NAAGI. The 50th word in NAAIG.

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