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

2. How many ways are there to put 5 balls in 3 boxes if the balls are not distinguishable and neither are the boxes?

OkNietzsche Feb 15, 2019

#1**+3 **

Assuming that some boxes could remain empty.....

For the first one....let the number of balls = k and the number of boxes = n

So...we have

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

For the second one.....we have the following partitions of 5 indistinguishable balls in 3 indistinguishable boxes

5, 0, 0

4, 1, 0

3, 2, 0

3, 1, 1

2, 2, 1 = 5 ways

CPhill Feb 15, 2019