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.
+129847 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%
