Question

1. There are 12 teachers. Three are selected to lead the field trip. How many different groups of three teachers can be formed?
A.22
B.440
C.220
D.44
2.How many different committees of 3 can be formed if you have 6 volunteers to choose from?
A.10
B.120
C.40
D.20
3. As a freshman in high school, a student is given two electives. The student can choose from art, band, choir, computer applications, wood shop, auto shop, and drama. How many different ways could a student choose their electives?
A.14
B.21
C.35
D.42

Answer 1

1. The required number of combinations of teachers taken 3 at a time is given by:
\[12C3=\frac{12!}{3!9!}=\frac{12\times11\times10}{3\times2}=you\ can\ calculate\]

Answer 2

220

Answer 3

Good work! You are correct.
2. the number of different committees of three is given by:
\[6C3=\frac{6!}{3!3!}=\frac{6\times5\times4}{3\times2}=you\ can\ calculate\]

Answer 4

54

Answer 5

Not really. Can you check your calculation?

Answer 6

wait

Answer 7

20

Answer 8

Correct!
3. The required number of choices of two electives out of the seven available is given by:
\[7C2=\frac{7!}{2!5!}=\frac{7\times6}{2}=you\ can\ calculate\]

Answer 9

21

Answer 10

You are correct! Good work :)