Question

    In how many different ways can the letters of the word

    MOTHER be arranged so that the vowels are always together?
    A 223 Correct Answer Incorrect Answer
    B 200 Correct Answer Incorrect Answer
    C 240 Correct Answer Incorrect Answer
    D 273 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    MOTHER has 6 letters: M, O, T, H, E, R Vowels: O, E Treat the pair of vowels as a single block: (OE or EO). So we have 5 objects to arrange: [vowel-block], M, T, H, R Number of ways to arrange 5 distinct objects = 5! = 120 Within the vowel-block, O and E can be arranged in 2! = 2 ways. Total arrangements = 5! × 2! = 120 × 2 = 240

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