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    Question

    In how many ways can the letters of the word ‘MEDICAL’ be rearranged so that the vowels never come together?

    A 4330 Correct Answer Incorrect Answer
    B 4340 Correct Answer Incorrect Answer
    C 4350 Correct Answer Incorrect Answer
    D 4320 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Total number of letters in the word ‘MEDICAL’ = 7 The word MEDICAL consists of 7 letters in which E, I and A are three vowels. We get MDCL (EIA) keeping EIA together as single entity. Number of ways the letters can be formed when vowels are together = 5! × 3! = 720 Required number of arrangements when vowels are never together = 7! - 720 = 5040 – 720 = 4320

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