How many ways are there to distribute 6 balls into 3 boxes i

How many ways are there to distribute 6 balls into 3 boxes if

a. both the balls and boxes are labeled?

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

c. The balls are unlabeled, but the boxes are labeled?

d. both the boxes and balls are unlabeled?

Noe that boxes may be empty in all of these situations.

Solution

3^5

C(5,5)

3!5!C(5,5)

C(3,5)