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    Question

    Five singers are to be arranged in a line for a concert

    photo. Two of them are siblings and must not stand next to each other. How many valid arrangements are possible?
    A 96 Correct Answer Incorrect Answer
    B 84 Correct Answer Incorrect Answer
    C 72 Correct Answer Incorrect Answer
    D 64 Correct Answer Incorrect Answer
    E 60 Correct Answer Incorrect Answer

    Solution

    5 singers can be arranged among themselves in 5P5 ways = 120 ways.
    Assume that the 2 siblings are one entity. The total number of ways in which they can be arranged among themselves = 2! = 2 ways.
    Also, the set of two siblings and the other students can be arranged among themselves = 4! = 24 ways.
    Thus, total number of ways in which two siblings are together = 2 × 24 = 48
    Thus, number of ways in which the siblings will not stand together = 120 − 48 = 72

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