When selecting one or more identical balls from multiple colors, the number of ways is found by considering the choices for each color independently. For each color, you can choose any number from 0 to the total available. The total ways to choose balls (including selecting none) is calculated by multiplying one more than the count for each color: (10+1) for white, (9+1) for green, and (7+1) for black. This gives $11\times 10\times 8=880$. Since we must select at least one ball, we subtract the one case where no balls are selected.

Final answer: $880-1=879$