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 :
(1) 880 (2) 629 (3) 630 (4) 879

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 :
(1) 880 (2) 629 (3) 630 (4) 879

anonymous · Answer

$$(10+1) \times (9+1) \times (7+1) -1 = 879 $$

anonymous · Answer

can you explain it properly? why not 10 x 9 x 7 ??

anonymous · Answer

For $n $ identical balls (balls of same color) you can select none or more them in $ (n+1)$ ways.

anonymous · Answer

okay...then why -1 in the end?

anonymous · Answer

Because this include the case where we select none from all of the groups but the question ask for one or more, hence we need to subtract 1 at last.

anonymous · Answer

Ah! I see. Thanks a lot! :)