How many ways are there to put 6 toys in 3 boxes if the toys are not distinguishable but the boxes are?
The only relevant thing is how many toys go into each box :)
I get
Count | Box1 | Box2 | box3 |
1 | 6 | 0 | 0 |
2 | 5 | 1 | 0 |
3 | 5 | 0 | 1 |
4 | 4 | 2 | 0 |
5 | 4 | 1 | 1 |
6 | 4 | 0 | 2 |
7 | 3 | 3 | 0 |
8 | 3 | 2 | 1 |
9 | 3 | 1 | 2 |
10 | 3 | 0 | 3 |
11 | 2 | 4 | 0 |
12 | 2 | 3 | 1 |
13 | 2 | 2 | 2 |
14 | 2 | 1 | 3 |
15 | 2 | 0 | 4 |
16 | 1 | 5 | 0 |
17 | 1 | 4 | 1 |
18 | 1 | 3 | 2 |
19 | 1 | 2 | 3 |
20 | 1 | 1 | 4 |
21 | 1 | 0 | 5 |
22 | 0 | 6 | 0 |
23 | 0 | 5 | 1 |
24 | 0 | 4 | 2 |
25 | 0 | 3 | 3 |
26 | 0 | 2 | 4 |
27 | 0 | 1 | 5 |
28 | 0 | 0 | 6 |