math

There are 5 boys and 4 girls in my class.

In how many ways can they be seated in a row of 9 chairs such that at least 2 boys are next to each other?

In how many ways can they be seated in a row of 9 chairs such that at least 3 girls are all next to each other?

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asked by Speedo
  1. number of ways for them to sit without any restriction
    = 9! = 362880
    Let's calculate the number of ways for none of the boys to be together.
    that can only happen this way
    BGBGBGBGB
    number of such ways
    = 5x4x4x3x3x2x2x1 = 2880

    So the number of ways with at least 2 boys together
    = 362880-2880 = 360000

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    posted by Reiny

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