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    Question

    How many distinct arrangements of DAUGHTER are there if

    the vowels remain together?
    A 4650 Correct Answer Incorrect Answer
    B 4840 Correct Answer Incorrect Answer
    C 4320 Correct Answer Incorrect Answer
    D 4660 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, Vowels = A, U, E Consonants = D, G, H, T, R (all distinct) Items = 1 (vowel block) + 5 = 6 (all distinct) Arrangements = 6! = 720 Arrangements of vowels = 3! = 6 Total words = 720 × 6 = 4320

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