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

    Question

    Five students are to be arranged on five chairs for a

    photograph. Three of these are girls and the rest are boys. Find out the total number of ways in which three girls are not together.
    A 96 Correct Answer Incorrect Answer
    B 90 Correct Answer Incorrect Answer
    C 84 Correct Answer Incorrect Answer
    D 78 Correct Answer Incorrect Answer

    Solution

    5 students can be arranged among themselves in 5P5 ways = 120 ways.
    Assume that the 3 girls are one entity. The total number of ways in which they can be arranged among themselves = 3! = 6 ways.
    Also, the set of three girls and the other students can be arranged among themselves = 3! = 6 ways.
    Thus, total number of ways in which three girls are together = 6 × 6 = 36
    Thus, number of ways in which all 3 girls will not occupy consecutive seats = 120 − 36 = 84

    Practice Next
    More Permutation and combination Questions

    Relevant for Exams:

    ask-question