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

If there are no restrictions, then:

 

[6 + 3 - 1] C [3 - 1] =8C2 =28 different ways.

I am a bit rusty on these but this appears to be a standard 'stars and bars' problem.

You can look that up if you want, there are some good videos on it around the place.

the balls are all the same so the only difference is how many balls are in each different box.

 

The balls are all the same, put them in a row.  Now you are going to seperate them with 2 bars.

The ones in front of the front bar gointo box1, whe ones between the bars go in box2 and the ones after the last bar go into box three

Draw a pic to see what I am talking about.

 

So now you have 6 stars and 2 bars and you just need to know how many different pleaces those bars can be put so that will be

choose 2 from 8         

8C2 = 28 ways

 

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If the boxes had alos been the same, which they weren't then...

006      

015

024

033

114

123

222

That is all I can see,  I think there would only be 7 ways .