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    Question

    Find the no. of words formed by using all the letter of

    the word DISCOUNT, so that the vowels are never together?
    A 42000 Correct Answer Incorrect Answer
    B 36000 Correct Answer Incorrect Answer
    C 24000 Correct Answer Incorrect Answer
    D 32000 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Total number of words formed by using all the letters of the given word = 8! = 8 ×  7 × 6 × 5 ×  4 ×  3 ×  2 ×  1 = 40320 Number of words formed when vowels are together = DISCOUNT = 3! ×  6! = 6 x 720 = 4320 Number of words formed when vowels are never together = 40320 – 4320 = 36000

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