Find the number of ways to put 8 distinguishable balls in 3 indistinguishable boxes.
Find the number of ways to put 8 indistinguishable balls in 3 indistinguishable boxes.
For the first we need something known as Stirling Numbers of the second kind
S (8, 3) = 966 ways
For the second we want to partition the integer 8 into 3 parts
This is
P(8,3) =
8 0 0
7 1 0
6 2 0
5 3 0
4 4 0
6 1 1
5 2 1
4 3 1
4 2 2
3 3 2
10 ways
