The planning committee at school has 11 members. Exactly five of these members are teachers. A four-person subcommittee with at least one member who is not a teacher must be formed from the members of the planning committee. How many distinct subcommittees are possible?

Answer 1

so you have 5 teachers and 6 non-teachers
the cases you DON'T want is the case where all 4 that are selected are teachers
number of selections with no restrictions = C(11,4)
number of selections with all teachers = C(5,4)

so number of selections as stated = ....

Answer 2

So the answer is 325

Answer 3

its not gud 2 give answers w/out explaining

Answer 4

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

Answer 5

You guys copied this off alcumus. Stop cheating.