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    Question

    Find the number of ways to arrange each letter of the

    word 'AGRICULTURE' such that all the vowels always come together.
    A 60,480 Correct Answer Incorrect Answer
    B 1,25,000 Correct Answer Incorrect Answer
    C 1,51,200 Correct Answer Incorrect Answer
    D 1,77,120 Correct Answer Incorrect Answer

    Solution

    Number of letters = 11
    Take all the vowels (AIUUE) as one entity.
    Number of letters now = 6 + 1 = 7!
    Number of ways to arrange all the letters = 7! ├╖ 2! = 5040 ├╖ 2 = 2,520
    Number of ways to arrange vowels = 5! ├╖ 2! = 120 ├╖ 2 = 60
    Required number of ways = 2,520 ├Ч 60 = 1,51,200

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