Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is:

For identical items of $p$ types, $q$ types, and $r$ types, the number of ways to select zero or more items is $(p+1)(q+1)(r+1)$.Here, $p=10,q=9,r=7$.Total ways (including selecting zero balls) $=(10+1)(9+1)(7+1)=11\times 10\times 8=880$.To select "one or more" balls, we subtract the case where no balls are selected (1 way).Total ways $=880-1=879$.