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 There is a gorup of five children, where two of the children are twins.  In how many ways can I distribute 7 identical pieces of candy to the children, if the twins must get an equa amount of candy?

 Dec 15, 2022
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Children a, b, c, and 2t need 7 identical candies:

Case 1: t = 0

a + b + c = 7, nonnegative a and b and c: stars and bars = 9 choose 2 = 36

Case 2: t = 1

a + b + c = 5, nonnegative a and b and c: stars and bars = 7 choose 2 = 21

Case 3: t = 2

a + b + c = 3, nonnegative a and b and c: stars and bars = 5 choose 2 = 10

Case 4: t = 3

a + b + c = 1, nonnegative a and b and c: stars and bars = 3 choose 2 = 3

36 + 21 + 10 + 3 = 70 total ways.

 Dec 15, 2022

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