There is a group of five children, where two of the children are twins. In how many ways can I distribute 8 identical pieces of candy to the children, if the twins must get an equal amount of candy?

Answer 1

Let's consider the twins as one entity for the distribution of candy. This reduces the problem to distributing 8 identical pieces of candy to 4 entities (3 individual children and one entity representing the twins).

We can use the stars and bars method to solve this problem. There are 8 candies and 3 "dividers" to separate them into 4 entities. The number of ways to distribute the candies is then:

C(8 + 3, 3) = C(11, 3) = 165

Therefore, there are 165 ways to distribute the 8 pieces of candy to the children, with the twins receiving an equal amount.