Question

6 teachers and 12 students volunteer for a committee to discuss extra curricular activities. How many committees of 5 people can be made if barry and miss morrison cannot be on the committee togetehr

Answer 1

Since Barry and Miss Morrison cannot be on the committee together, we have to consider two cases: one where Barry is on the committee and Miss Morrison is not, and one where Miss Morrison is on the committee and Barry is not.

Case 1: Barry is on the committee and Miss Morrison is not.
In this case, we have to select 4 more people from the remaining 6 teachers and 12 students, excluding Miss Morrison. The number of ways to choose 4 people from 6 teachers and 12 students is given by the combination formula: C(6+12-1, 4) = C(17, 4) = 2380.

Case 2: Miss Morrison is on the committee and Barry is not.
Similarly, in this case, we have to select 4 more people from the remaining 6 teachers and 12 students, excluding Barry. The number of ways to choose 4 people from 6 teachers and 12 students is again given by the combination formula: C(6+12-1, 4) = C(17, 4) = 2380.

Thus, there are a total of 2380 + 2380 = 4760 committees of 5 people that can be made if Barry and Miss Morrison cannot be on the committee together.