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

 Nov 5, 2019
 #1
avatar+105919 
+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

 Nov 5, 2019
 #4
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+1

omg thank you so much!

Guest Nov 6, 2019
 #2
avatar+105919 
+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

 Nov 5, 2019
 #3
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+1

thank you so much!!

 Nov 6, 2019

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