Combinations, Permutations, and Counting Principles

Kayleigh, Chloe, and Brandon are planning a movie night during their vacation. They have a collection of 20 DVDs purchased over the past year. They decided to watch five movies in one night. How many different sets of five DVDs can they choose for their movie night?

(a)  

• Combination

• Permutation

• Counting Principles

• Factorial

The model of car you are thinking of purchasing is available in nine different colors, three different styles and two sizes of motor. How many ways can you order the car?

Mathematical Equivalence

ON

A disc jockey 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?

Mathematical Equivalence

ON

Nicole has four different skirts, three different blouses and two pairs of shoes which she can wear for a business meeting. In how many ways can Nicole dress for the meeting?

Mathematical Equivalence

ON

How many ways can a stylist arrange 5 of 8 vases from left to right in a store display?

Mathematical Equivalence

ON

Members of 6 different school organizations decorated floats for the homecoming parade.  How many different ways can first, second, and third prize be awarded?

Mathematical Equivalence

ON

Adriana, Emma, and Caleb are helping their friend Riley to submit 4 paintings as part of her application to art school. If Riley has 25 paintings to choose from, how many ways can she pick 4?

• 12,650

• 303,600

• 100

• 254

Natalina, Caleb, and Emma are part of a softball team of 17 players. They need to choose three players to refill the water cooler. How many different combinations of players can they choose?

• 272

• 4080

• 680

In a class of 12 students, John, Tim, Adriana and their friends are electing a President, Vice-President, and Secretary. What is the method used to determine the number of ways these positions can be filled?

• Permutation

• Combination

• Neither

Kayleigh, Caleb, and Morgan are part of a school club with 10 members. The club needs to select a team of three for an upcoming event. The method used to select the team is a (a)   .

• Permutation

• Combination

• Neither