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

Guest Nov 5, 2019

#1**+2 **

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

Melody Nov 5, 2019

#2**+2 **

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

Melody Nov 5, 2019