houstonrockets16 wrote:In a certain group of ten members, 4 teach french, and the rest teach spanish or german. if a group of 3 is chosen, and at least one must teach french; how many committes can be chosen?
100
please tell me how!! thanks!
In combinatorics, when you see the words "at least", most of the time it is easier to think of the complement. In our case, the complement of at least one must teach french is none teaches french. If you can find the # of ways forming the committee with no one teaching french, subtract that from the # of ways of forming the committee when there is no restrictions to get your answer.
Choose 3 from 10: 10C3
Choose 3 from the 6 that don't teach french: 6C3
Therefore 10C3 - 6C3 = 120 - 20 = 100
Different approach, but same answer.
