In a recent discussion of a variation of chess, someone stated to me that it is not possible to calculate the number of legal arrangements of KQP vs KQ without generating a list of all possible arrangements of these five pieces on the board and then going thru and eliminating the illegal ones (both kings in check, etc.). In the variation we were discussing, the board was 10x8, rather than the traditional 8x8. There are other rule changes, but none that affect this calculation. I claim that it is possible, but very difficult. Could anyone help us to resolve this issue?

Thanks,
Thad