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There is a group of five children, where two of the children are twins.  How many ways can I distribute 10 identical pieces of candy to the children, if the twins must get an equal amount of candy?

 Jan 5, 2023
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1 - If each twin gets "0" candies, then there are: [10 + 3 -1] C [3 - 1] ==66 ways

 

2 - ........................   1  ........................................: [8 + 3 - 1] C [3 - 1] ==45 ways

 

3 - ........................  2  .........................................: [6 + 3 - 1 ] C [3 - 1] ==28 ways

 

4 - ........................  3  .........................................: [4 + 3 - 1] C [3 - 1] == 15 ways

 

5 - ........................  4...........................................: [2 + 3 - 1] C [3 - 1] == 6 ways

 

6 - ........................  5  ..........................................: [0 + 3 - 1] C [3 - 1] == 1 way

 

7 - Total number of ways ==[66 + 45 + 28 + 15 + 6 + 1] ==161 ways

 Jan 5, 2023

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