1. How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable and neither are the boxes?

2. How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable but the boxes are?

Guest Jun 25, 2019

#1**+1 **

1. How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable and neither are the boxes?

Assuming that we can have empty boxes.....this boils down to the number of ways that we partition 6 identical balls into 3 identical boxes

These are

6, 0, 0

5, 1, 0

4, 2, 0

4, 1, 1

3, 3, 0

3, 2, 1

2, 2, 2

So......7 ways

CPhill Jun 26, 2019

#2**+1 **

2. How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable but the boxes are?

Again....assuming that we can have empty boxes.....the number of ways of distributing k identical balls into n distinguishable boxes is given by :

C ( k +n - 1 , n - 1) = C (6 +3 - 1, 3 - 1 ) = C (8,2) = 28 ways

CPhill Jun 26, 2019