Combinations and Arrangements: A Counting Challenge

A bakery has 5 different types of cupcakes. How many ways can they arrange 3 types of cupcakes on a display stand?

• 15

• 5

• 20

• 10

In a class of 10 students, how many ways can a teacher select a president, vice president, and secretary?

• 360

• 720

• 540

• 1000

A sports team has 8 players. How many different ways can the coach choose 4 players to start the game?

• 56

• 70

• 28

• 84

A password consists of 4 letters followed by 2 digits. How many different passwords can be created if letters can be repeated but digits cannot?

• 675000

• 676100

• 676000

• 700000

A book club has 6 members. How many ways can they form a committee of 3 members?

• 30

• 20

• 10

• 15

A concert has 7 different acts. How many ways can the acts be arranged on the schedule?

• 1000

• 720

• 4032

• 5040

In a race with 12 participants, how many ways can the top 3 finishers be arranged on the podium?

• 720

• 1440

• 1100

• 1320

A pizza shop offers 4 different toppings. How many ways can a customer choose 2 toppings for their pizza?

• 4

• 8

• 10

• 6

A school is organizing a field trip for 15 students. How many ways can they select a group of 5 students to go?

• 45

• 150

• 500

• 3003

A library has 9 different books. How many ways can a student choose 3 books to take home?

• 45

• 84

• 27

• 36