Counting Principle Permutations Combinations

Ten marching bands qualified for finals. If their performance order is random, how many ways can the final four performances be listed?

• 5,040

• 720

• 24

• 40

A dessert is made by choosing from a type of ice cream (chocolate, vanilla, or strawberry),

a topping (sprinkles, gummies, nuts, bananas), and a sauce (caramel, hot fudge).

How many different sundaes can be made?

• 24

• 9

• 81

• 12

How many unique ways can you flip a coin, roll a die, and spin a five-sectioned spinner?

• 3

• 13

• 30

• 60

A four-unit passcode is created by choosing two digits and then two letters. How many unique passcodes exist if no number or letter can be repeated?

• 16

• 10,000

• 58,500

• 67,600

How many unique "words" can be made from all the letters in SPARTANS?

• 5,040

• 10,080

• 40,320

• 80,640

How many unique "words" can be made from all the letters in TURKEY?

• 6

• 60

• 72

• 720

• 2

• 24

• 1,680

• 40,320

Evaluate ₁₀P₃

• 3,628,800

• 5,040

• 720

• 120

Evaluate ₁₂C₄

• 479,001,600

• 40,320

• 11,880

• 495

Evaluate ₅P₅

• 120

• 60

• 5

• 1