Question

Suppose that 3 teachers and 6 students volunteered to be on a graduation committee. The committee must consist of 1 teachers and 2 students. How many different graduation committees does the principal have to choose from? 45 60 C. 90 D. 180

Answer 1

The principal has 45 different graduation committees to choose from.

Step-by-step explanation:

To determine the number of different graduation committees the principal has to choose from, we need to use the concept of combinations. Since there are 3 teachers and 6 students, the principal can choose 1 teacher from 3 options and 2 students from 6 options.

The number of ways to choose the teacher is C(3, 1) = 3. This means there are 3 different choices for the teacher.

The number of ways to choose the students is C(6, 2) = 15. This means there are 15 different choices for the students.

To find the total number of different graduation committees, we multiply the number of choices for the teacher by the number of choices for the students: 3 x 15 = 45.

Therefore, the principal has 45 different graduation committees to choose from.