How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable but the boxes are?
How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable but the boxes are?
Number in the boxes
6,0,0 3 ways
5,1,0 6 ways
4,2,0 6 ways
4,1,1 3 ways
3,2,1 6 ways
3,3,0 3 ways
2,2,2 1 ways
I get 28 ways
The other method is the stars and bars method
There are 6 stars, they are seperated into 3 groups so we need 2 bars to seperate them
One group is before the bars, one is after and the other is inbetween
so that is 8 'things' and I need to find how many different places the bars can go.
That is
8C2=28