Evaluate the expression. 4! • 3!

12
30
144 ANSWER
5,040

Eight students are competing for a blue, red, and yellow ribbon for their agriculture project.

How many different ways are there to present those ribbons if the order matters?

56
336 ANSWER
6,720
8,064

Three out of seven students in the cafeteria line are chosen to answer survey questions.

How many different combinations of three students are possible?

7 C 3 = StartFraction 7 factorial Over (7 minus 3) factorial 3 factorial

7
35 ANSWER
70
210

A membership committee of three is formed from four eligible members. Let the eligible members be represented by A, B, C, and D. The possible outcomes include S = {ABC, ABD, ACD, BCD}.

Which statements about the situation are true? Select three options. 1, 2,4

There are four ways to choose the committee.
There are three ways to form the committee if person D must be on it.
If seven members are eligible next year, then there will be fewer combinations.
If persons B and C must be on the committee, there are two ways to form the committee.
If persons A and C must be on the committee, then there is only one way to form the committee.

Three out of nine students in the computer club are getting prizes for first, second, and third place in a competition.

How many ways can first, second, and third place be assigned?

9 P 3 = StartFraction 9 factorial Over (9 minus 3) factorial

3
84
504 ANSWER
2048

Fiona needs to choose a five-character password with a combination of three letters and the even numbers 0, 2, 4, 6, or 8.

If she uses her initials, F, J, and S in order as the first three characters, and she does not use the same digit more than once in her password, how many different possible passwords are there?

10
20 ANSWER
24
40

Four band members, Harry, Isabel, Jose, and Karen, are all boarding a bus to attend a concert. In each arrangement below, the first initial of each person’s name represents that person’s position as he or she boards the bus: first, second, third, and fourth.

If we know that Karen boards the bus first, which shows the possible outcomes for this event?

KHIJ NOT A
KHIJ, KHJI
KHIJ, KHJI, KJHI, KJIH
KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH