Counting Principle Permutations Combinations

Runners finishing 1st, 2nd, and 3rd in a race.

• Permutation

• Combination

Justin took a quiz with five multiple choice (A-D) and five true/false questions. How many different ways can he answer the questions?

• 1024

• 32

• 32768

• 25

Arranging letters to make a password.

• Permutation

• Combination

How many ways can you arrange the letters in the word FACTOR?

• ₆P₆=720

• ₆C₆=1

• 6 x 5 = 30

• 120 ways

How many ways can two jellybeans be chosen from a bag of 15 unique jellybeans.

• ₁₅C₂=105

• ₁₅P₂=210

• 15 x 2 = 30

• 100 ways

How many ways can 5 books be arranged on a shelf?

• 10

• 120

• 1

• 5

At  a New Car Dealership a particular model comes in 4 trim levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?

• 180

• 23

• 12

• 60

A menu has 6 different sandwiches, with 3 choices of potato chips, 3 types of salad and 5 different beverages. How many different lunch combinations consisting of a sandwich, chips, salad, and beverage can be ordered?

• 30

• 17

• 90

• 270

There are 18 students playing Quizizz in math class. How many ways can they win the gold, silver, and bronze places on the podium?

• 54

• 816

• 5832

• 4896

Homecoming has 7 candidates for King. How many ways can a King and a First Runner-up be chosen to form the Festival Court?

• 23

• 840

• 42

• 3,628,800