Six teachers and 12 students volunteer for a committee to discuss extra-curricular activities. How many committees of 5 people can be made if: a) there must be exactly 3 students on the committee

b) there must be at least one teacher and at least one student on the committee

a) 11,880

b) 7,770

Step-by-step explanation:

The number of teachers that volunteer = 6 teachers

The number of students that volunteer = 12 students

The number of people in the committee = 5 people

a) The exact number of student on the committee = 3 student

Therefore, the number of teachers in the committee of 5 = 5 - 3 = 2

The number of teachers in the committee = 2 teachers

We get;

The number of committees that can be made = ₁₂C₃ × ₆C₂ = 792×15 = 11,880

b) When there is at least one teacher and at least one student on the committee, we have;

₁₂C₄ × ₆C₁ + ₁₂C₃ × ₆C₂ + ₁₂C₂ × ₆C₃ + ₁₂C₁ × ₆C₄ = 7,770

The number of committees having at least one teacher and at least one student = 7,770

the best buy, is the 4- kilogram bag of lollipops for $18.40.

step-by-step explanation:

i found my answer by dividing the cost of each bag by their respective weights.

14.88 divided by 2 = 7.44

17.29 divided by 3 = 5.77

18.4 divided by 4 = 4.6

24.4 divided by 5 = 4.88

by this, i found that the 4 kilo bag is the best buy.

4444444444444 i think