A student council consists of 15 students. Two council members have the same major and are not permitted to serve together on a committee.

How many ways can a committee of five be selected from the membership of the council?

Answer: 4004ways

Step-by-step explanation:

Total number of Students = 15

Total number of students to be on the committee = 5

Since two members are of the same major and must not be on the committee, then we are left with choosing 5 people from just 14 People after we eventually remove one from those two students with same majors.

Hence to select 5 people from 14 people, we use the combination formula 14C5.

From the two students with same major we also use the combination Formula in knowing the number of ways any of the two students can be chosen. To choose one from these two students, we use the combination Formula 2C1.

Hence, the total number of ways to choose the committee of 5 and ensuring the two students with same major aren't on the committee becomes:

= 14C5 * 2C1

= 2002 * 2

= 4004ways.