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21 December, 13:01

In how many ways can 12 one-dollar coins be shared between Josh, Frank, and Suzy if each of them receives at least 3 coins?

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  1. 21 December, 13:52
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    Since 9 of the coins are accounted for (each must receive at least 3) let's see how we can divide the remaining 3 coins.

    Josh Frank Suzy

    3 0 0 Josh gets all of them

    0 3 0 Frank gets all of them

    0 0 3 Suzy gets all of them

    1 1 1 They share them

    2 1 0 2 way to do it if Josh gets 2 coins

    2 0 1 (this is the 2nd way if Josh gets two)

    So there must be two ways to do it if Frank gets 2 coins and two more ways to do it if Suzy gets two coins.

    Recap: 3 way if one person gets all 3 coins and the others get 0

    1 way if they all get a single coin

    6 ways if one person gets 2 and another gets the remaining one.

    Total = 10 ways.
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