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    Question

    In how many different ways can the letters of the word

    "AIRSTRIKE" be arranged if all the vowels must always be grouped together?
    A 720 Correct Answer Incorrect Answer
    B 1440 Correct Answer Incorrect Answer
    C 2160 Correct Answer Incorrect Answer
    D 4320 Correct Answer Incorrect Answer
    E 5040 Correct Answer Incorrect Answer

    Solution

    The word “AIRSTRIKE’’ contains 9 letters with 4 vowels, (A, 2I, 2R, S, T, K, E)

    If vowels comes together, then 4 vowels will behave as a single entity, so, remaining 5 consonants and this entity, a total of 6 letters will arrange themselves in 6! Ways, and 4 vowels will arrange themselves in

    (4!/2!) Ways, as there are 2I,

    So, total number of ways of arranging letters of the word ‘“AIRSTRIKE’’ such that all the vowels always come together = (6!/2!) × (4!/2!) = 360 × 12 = 4320

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