Counting Principle, Permutations and Combinations

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

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

Suppose a club has 20 members. In how many different ways could the club choose a president, vice-president, and secretary?

• 6

• 60

• 1140

• 6840

Suppose that you have 12 books that are all different from each other. You've decided to let a friend borrow 3. How many different ways could your friend decide which books to borrow?

• 36

• 1728

• 1320

• 220

"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

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

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