Permutation, Combinations, and Counting

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

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

• 56

• 336

• 24

• 512

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

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

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

What is the value of 8!

• 40320

• 36

• 362880

• 5040

Which of the following is an example of combination?

• Form a passcode with 4 digits
• Students line up in a queue to assembly
• Choose 4 students in a class committee
• Choose the chairperson, secretary and treasurer in a club

Find the number of possibilities:
A team of 17 softball players needs to choose three players to refill the water cooler.

• 272
• 4080
• 680

A DJ has to choose three songs for the last few minutes of his evening show. If there are nine songs that he feels are appropriate for that time slot, then how many ways can he choose and arrange to play three of those nine songs?

Is this a Permutation or Combination?

• Permutation - the order of the songs matters

• Combination - the order of the songs does not matter

The ski club has 10 members and is choosing three officers for the season. How many ways can they pick a captain, co-captain and secretary?

Is this a Permutation or a Combination?

• Permutation - the order matters

• Combination - the order does not matter