Combinations Permutations Counting Principle

In how many different ways can a coach name the first three batters in a nine-batter baseball lineup?

• 168

• 504

• 27

• 84

There are six roads connecting Midland to Bay City.  There are five roads connecting Bay City to Port Huron.  If you travel from Midland to Port Huron, through Bay City, how many possible routes are there?

• 720

• 6

• 30

• 11

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

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

• 3

• 13

• 30

• 60

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