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Math Help - More questions on splitting 18 children into 3 groups

  1. #1
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    More questions on splitting 18 children into 3 groups

    1) How many ways can 18 children be split into 3 teams: Man U, Arsenal and Chelsea? (The split doesn't have to be equal and a team can be empty).

    My attempt:
    18! * the no. of ways of arranging 3 a's and 18 b's. But I'm not sure how many this is. Is it 20 choose 2?

    2) No. of ways to split 18 identical footballs among Man U, Arsenal and Chelsea?

    3) 18 identical footballs. 5 different teams. No team should receive more than 5 balls.

    Thanks so much
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  2. #2
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    Quote Originally Posted by durrrrrrrr View Post
    1) How many ways can 18 children be split into 3 teams: Man U, Arsenal and Chelsea? (The split doesn't have to be equal and a team can be empty).
    I donít know the exact meaning of the phrase ďa team can be emptyĒ.
    If it means that all twenty could be assigned to Manchester United then you are simply counting the number of functions from a set of twenty to a set of three.
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