Helen and Patty both belong to a club of 25 members. A committee of 4 is to be selected at random from the 25 members. Find the probability that both Helen and Patty will be selected.
We are just countng sets, here......
The total possible sets formed from choosing 4 members from 25 is C(25,4) = 12650
However.......we are only interested in the sets that contain both Helen and Patty......so.....we want to choose any 2 other members from the remaining 23 = C(23,2) = 253
So....the probability that both Helen and Patty are chosen = 253 / 12650 =
1/50 = .02 = 2%