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?
+1624 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.
