Question

You want to distribute 7 candies to 4 kids. If every kid must receive at least one candy, in how many ways can you do this?

Answer 1

20

Explanation:

Once you give 1 candy to each of the 4 kids, you will have 3 remaining. The number of ways those can be distributed to 4 kids is given by ...

(n+k-1)C(n)

where n is the number of candies, and k is the number of kids. "aCb" is the number of ways a can be taken b at a time:

aCb = a!/(b!(a-b)!)

For n=3 and k=4, this is ...

(3+4-1)C(3) = 6C3 = 6!/(3!·3!) = 20

There are 20 ways to distribute 7 candies to 4 kids so that each kid receives at least one.