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    Question

    In how many ways can 5 boys and 3 girls be arranged in a

    row so that no two girls sit together?
    A 720 Correct Answer Incorrect Answer
    B 2,880 Correct Answer Incorrect Answer
    C 14,400 Correct Answer Incorrect Answer
    D 17,280 Correct Answer Incorrect Answer

    Solution

    ATQ, Arrange 5 boys first: 5! = 120 ways. This creates 6 possible gaps for girls: _ B _ B _ B _ B _ B _ тЖТ 6 gaps. Choose 3 of these 6 gaps for the 3 girls: C(6,3) = 20. Arrange 3 girls among themselves: 3! = 6. Total arrangements = 5! ├Ч C(6,3) ├Ч 3! = 120 ├Ч 20 ├Ч 6 = 14,400.

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