Question

How many ways are there to distribute five balls into three boxes if each box must have at least one ball in it if

a) both the balls and boxes are labeled?

b) the balls are labeled, but the boxes are unlabeled?

c) the balls are unlabeled, but the boxes are labeled?

d) both the balls and boxes are unlabeled?​

Answer 1

Answer:

We have to distribute 5 distinct balls into 3 identical boxes. Thus, n = 5 and k = 3. Therefore, there are a total of 41 possibilities.