I have 6 identical pieces of candy to distribute to a group of 5 children. Two of the children in the group are twins, and they insist on receiving an equal amount of candy. How many ways can I distribute the candy?

hugomimihu Mar 17, 2020

#1**0 **

Using casework, there are C(7,3) + C(5,3) + C(3,3) = 35 + 10 + 1 = 46 ways to distribute the candies.

Guest Mar 19, 2020

#2**+3 **

Never mind, I found out how to do it, but it appears that your answer is wrong?

So I think we might use the hockey stick thereom thing...

it's C(n+k-1, k-1).

So if the twins each get 0, we have 6 candy, 6+(5-2)-1 = 8. 5-2-1=2. C(8,2).

We also get C(6,2), C(4,2), C(2,2), and c(0,2) with increasing values

Adding these together we get 50.

hugomimihu Mar 19, 2020