Combinations Permutations Counting Principle

Melanie is taking four classes this semester: American History, Algebra 2, AP English, and Chemistry. How many ways can these four classes be arranged on her schedule?

• 24

• 153

• 765

• 824

"The student body of 165 students wants to elect three representatives". Is this a permutation, combination, or neither?

• Combination

• Neither

• Permutation

Among the seven nominees for two vacancies on the city council are three men and four women. In how many ways may these vacancies be filled with any two of the nominees?

• 12

• 7

• 21

• 42

Use the fundamental counting principle to determine the number of ways a 4-digit pin number can be created if the first digit cannot be zero.

• 9000

• 40

• 39

• 90

In how many different ways can a committee of three people be selected from a total of eight?

• 56

• 336

• 24

• 512

An ice cream parlor has 15 different flavors. Michelle orders a sundae and has to select 3 flavors. How many different selections are possible?

• 2730

• 45

• 14,348,907

• 455

The manager of a 9 member baseball team must arrange the batting order. In how many ways can the manager of a baseball team arrange his players if there are no restrictions on the order?

• 81

• 362,880

• 18

• 387,420,489

A man has 8 pairs of pants, 12 shirts, 15 ties, and 6 sport coats. If he wears one of each, how many different outfits can he wear?

• 41

• 8640

• 2,430,480

• 101,270

There are 35 students on a football team. They must elect 3 students to serve as captains. How many different ways could the election turn out?

• 39,270

• 6545

• 105

• 42,875

From a class with 20 students, I need to select a group of 9 students to perform a top-secret mission. How many different ways can this group be selected?

• 167,960

• 60,949,324,800

• 180

• 362,880