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probability

there are 6 students(A-F)standing in a row,find the probability that any two of A,B and C do not stand next to each other.

4 girls and 8 boys are arranged in a row at random. Find the probability that any 2 girls do not stand next to each other.

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  • fooks
    Lv 7
    7 years ago
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    There are 6 students(A-F)standing in a row, find the probability thatany two of A,B and C do not stand next to each other.

    Solution :

    If the 6 students stand in a row without restriction :

    Number of ways = 6P6

    If any two of A, B and C do not stand next to each other :

    Firstly, arrange D, E and F (denoted as X) in a row (3P3­): _X_X_X_

    Then, Put A, B and C in any three spaces "_" (4P3).

    Number of ways = 3P3 x 4P3

    The required probability

    = 3P3 x 4P3 / 6P6

    = 3! x (4!/1!) / 6!

    = 1/5

    4 girls and 8 boys are arranged in a row at random.Find the probability that any 2 girls do not stand next to each other.

    Solution :

    If the 12 persons (4 girls and 8 boys) are arranged in a row withoutrestriction :

    Number of ways = 12P12

    If any 2 girls do not stand next to each other :

    Firstly, arranged the 8 boys (B) in a row (8P8) :_B_B_B_B_B_B_B_B_

    Then, Put the 4 girls in any 4 spaces "_" (9P4).

    Number of ways = 8P8 x 9P4

    The required probability

    = 8P8 x 9P4 / 12P12

    = 8! x (9!/5!) / 12!

    = 14/55

    Source(s): fooks
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