Counting Principle and Combinations

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

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

• Combination

• Neither

• Permutation

There are 10 students at a meeting. They each give a Graduation Day card to everyone else. How many cards were given?

• 10

• 1

• 90

• 3,628,800

In a primary election, there are four candidates for mayor, five candidates for city treasurer, and two candidates for county attorney. In how many ways may voters mark their ballots if they vote in all three of the races?

• 11

• 1

• 40

• 4

Suppose a True-False test has 20 questions. In how many ways may a student mark the test, if 7 questions are marked correctly and 13 incorrectly?

• 390,700,800

• 1,048,576

• 140

• 77,520

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