📢 Too many exams? Don’t know which one suits you best? Book Your Free Expert 👉 call Now!

    âš¡ Month End Offer - Flat 52% Off On All Courses! Enroll Now âš¡
    00:00:00 AM Left

    Question

    How many unique arrangements can be made using all the

    letters of the word "DELUSION", ensuring that the vowels do not appear together?
    A 32580 Correct Answer Incorrect Answer
    B 42420 Correct Answer Incorrect Answer
    C 37440 Correct Answer Incorrect Answer
    D 36240 Correct Answer Incorrect Answer
    E 38560 Correct Answer Incorrect Answer

    Solution

    If we take all the vowels to be a single letter, then

    Total number of letters = 5 [EUIO is taken as a single letter]

    Number of ways of arranging with all the vowels together = 5! × 4! = 120 × 24 = 2880

    Number of ways of arranging without any condition = 8! = 40320

    So, number of ways the word can be arranged so that all the vowels never occur together = 40320 – 2880 = 37440

    Practice Next
    More Permutation and combination Questions

    Relevant for Exams:

    ask-question