In that question, we have 10 distinguishable objects and 3 indistinguishable piles and one condition was also there that all piles should be non-empty.
Since we have indistinguishable piles so only numbers of objects matter not order e.g. 1,1,8 and 8,1,1 are the same thing.
| A | B | C | Calculation | total |
|---|
| 1 | 1 | 8 |
(C(10,8) * C(2,1) *C(1,1))/2
| 45 |
| 1 | 2 | 7 |
(C(10,7) * C(3,2) *C(1,1))
| 360 |
| 1 | 3 | 6 |
(C(10,6) * C(4,3) *C(1,1))
| 840 |
| 1 | 4 | 5 |
(C(10,5) * C(5,4) *C(1,1))
| 1260 |
| 2 | 3 | 5 |
(C(10,5) * C(5,3) *C(2,2))
| 2520 |
| 2 | 2 | 6 |
(C(10,6) * C(4,2) *C(2,2))/2
| 630 |
| 2 | 4 | 4 |
(C(10,4) * C(6,4) *C(2,2))/2
| 1575 |
| 3 | 3 | 4 |
(C(10,4) * C(6,3) *C(3,3))/2
| 2100 |
| | | TOTAL -----> | 9330 |
(A,B,C are indistinguishable only just name them for simplicity).
