Question

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 :(a) 880(b) 629(c) 630(d) 879

Answer 1

First, you can select from none to ten white balls. (10+1) choices.

Then, you can select from none to nine green balls. (9+1) choices.

Finally, you can select from none to seven red balls. (7+1) choices.

Putting this together, that is where the (10+1)(9+1)(7+1) derives.

However as you were asked to count selections of "one or more balls", you can not select none of all three colors at once (ie no balls at all). So that's what the −1 is about.

(10+1)(9+1)(7+1)−1