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

Question 1143352: How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable but the boxes are?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The first box can have 1, 2, 3, or 4 balls. It can't have 5 balls
because that would leave only 1 and a box is empty.
----------------------------------------------------------
1 in 1st box:
4, 1 ( other boxes )
1, 4
2, 3
3, 2
---------------
2 in 1st box:
3, 1 ( other boxes )
1, 3
2, 2
---------------
3 in 1st box:
2, 1 ( other boxes )
1, 2
---------------
4 in 1st box:
1, 1 ( other boxes )
---------------
I count 10 ways. I don't know how to express
this analytically. Feel free to get another opinion.
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