A bag contains r red and w white balls. A ball is selected at random, is removed, without replacement, until those of the same colour are left in the bag.

Find the probability that exactly one white ball left remains in the bag when the removal stops.

The solution says the (w-1) white balls have to be selected from (w+r-2), and thus the required probability is

( (r+w-2) choose (w-1) ) / ( (r+w) choose w )

Can anyone explain?

Thanks!