There are \( \left ( \begin{array}{c} 6 \\ 2 \end{array} \right) = 15 \) two-particle states, which we list with the total \( M \):
| Occupied | \( M \) | Occupied | \( M \) | Occupied | \( M \) |
| 1,2 | -4 | 2,3 | -2 | 3,5 | 1 |
| 1,3 | -3 | 2,4 | -1 | 3,6 | 2 |
| 1,4 | -2 | 2,5 | 0 | 4,5 | 2 |
| 1,5 | -1 | 2,6 | 1 | 4,6 | 3 |
| 1,6 | 0 | 3,4 | 0 | 5,6 | 4 |
There are 3 states with \( M= 0 \), 2 with \( M = 1 \), and so on.