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There is a group of five children, where two of the children are twins.  In how many ways can I distribute 17 identical pieces of candy to the children, if the twins must get an equal amount of candy?

 Jan 4, 2023
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a=listfor(n, 0/2, 18/2, (19 -2*n) nCr 2);print a, "=", sum a

 

(171, 136, 105, 78, 55, 36, 21, 10, 3 ) = 615 ways of distributing 17 candies to 3 kids + 2 twins.

 

171 ways of distributing the candies to the 3 remaining kids when the twins get "0" candies each

136 ............................................................................................................................ 1   ...................

105............................................................................................................................. 2   ..................

78 .............................................................................................................................. 3   ..................

55 .............................................................................................................................. 4   ..................

36 .............................................................................................................................. 5   ..................

21 ............................................................................................................................... 6   ..................

10 ............................................................................................................................... 7   ..................

3 ................................................................................................................................. 8   ..................

 Jan 4, 2023

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