The planning committee at school has 10 members. Exactly four of these members are teachers. A four-person subcommittee with at least one member who is a teacher must be formed from the members of the planning committee. How many distinct subcommittees are possible?

Guest Apr 13, 2021

#1**+1 **

Because there are 5 teachers on the committee, there are 6 non-teachers. Now, in total, we can form (11 \choose 4) = 330 subcomittees. The number of subcommittees with zero non-teachers is the number of subcommittees formed by the 5 teachers, totaling (5 \choose 4) = 5. So, the number of subcomittees with at least one non-teacher is 330 - 5 = 325

Mathdory Apr 13, 2021