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?
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
