Counting Principle

The Palace of Pizza offers small, medium, or large pizzas with 14 different toppings available. How many different 1-topping pizzas do they serve?

• 3 x 14 = 42

• 3 + 14 = 17

• 14 x 14 x 14 = 2744

• 14 x 13 x 12 = 2184

The letters A, B, C, and D are used to form four-letter passwords for entering a computer file. How many passwords are possible if letters can be repeated?

• 4 x 4 x 4 x 4 = 256

• 4 x 3 x 2 x 1 = 24

• 4 + 4 + 4 + 4 = 16

• 4 + 3 + 2 + 1 = 10

A restaurant serves 5 main dishes, 3 salads, and 4 desserts. How many different meals could be ordered if each has a main dish, a salad, and a dessert?

• 5 x 3 x 4 = 60

• 5 + 3 + 4 = 12

Marissa brought 8 T-shirts and 6 pairs of shorts to summer camp. How many different outfits consisting of a T-shirt and a pair of shorts does she have?

• 8 x 6 = 48

• 8 + 6 = 14

How many license plates consisting of three letters followed by three numbers are possible when no repetition is allowed?

• 26 x 25 x 24 x 10 x 9 x 8 = 11232000

• 26 x 26 x 26 x 10 x 10 x 10 = 17576000

• 26 x 25 x 24 x 9 x 8 x 7 = 7862400

• 26 x 26 x 26 x 9 x 9 x 9 = 12812904

There are 6 different packages available for school pictures. The studio offers 5 different backgrounds and 2 different finishes. How many different options are available?

• 6 x 5 x 2 = 60

• 5 x 2 = 10

• 6 + 5 + 2 = 13

How many 5-digit even numbers can be formed using the digits 4, 6, 7, 2, 8 if digits can be repeated?

• 5 x 5 x 5 x 5 x 4 = 2500

• 5 x 5 x 5 x 5 x 5 = 3125

• 5 x 4 x 3 x 2 x 1 = 120

How many license plate numbers consisting of three letters followed by three numbers are possible when repetition is allowed?

• 26 x 26 x 26 x 10 x 10 x 10 = 17576000

• 26 x 25 x 24 x 10 x 9 x 8 = 11232000

• 26 x 26 x 26 x 9 x 9 x 9 = 12812904

• 26 x 25 x 24 x 9 x 8 x 7 = 7862400

How many 4-digit positive even integers are there?

• 9 x 10 x 10 x 5 = 4500

• 10 x 10 x 10 x 10 = 10000

• 10 x 10 x 10 x 5 = 5000

• 5 x 5 x 5 x 5 = 625

How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

• 15
• 40
• 80
• 10