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4 December, 05:07

Suppose we want to divide the 10 dogs into three groups, one with 3 dogs, one with 5 dogs, and one with 2 dogs. how many ways can we form the groups such that fluffy is in the 3-dog group and nipper is in the 5-dog group?

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  1. 4 December, 05:32
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    420 ways

    Step-by-step explanation:

    According to the given statement:

    We want to divide the 10 dogs into three groups, one with 3 dogs, one with 5 dogs, and one with 2 dogs. How many ways can we form the groups such that fluffy is in the 3-dog group and nipper is in the 5-dog group.

    In this way we have 8 dogs left.

    2 spaces left in 3 dogs group

    4 spaces left in 5 dogs group

    and 2 spaces in 2 dogs group

    Therefore:

    = 8!/2!4!2!

    = 8*7*6*5*4*3*2*1/2*4*3*2*2

    = 8*7*6*5/2*2

    = 1680/4

    =420

    It means there are 420 ways to from the groups ...
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