Fundamental Principles of Counting

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

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

• 15

• 40

• 80

• 10

In Cornville, bicycle license plates have 2 letters followed by a 1-digit number. How many different license plates are possible?

• 6760

• 62

• 2600

• 6084

In the orchestra, there are eight violinists in the front row. How many different ways can they be seated?

• 40320

• 1

• 64

• 8

Which of the following situations is represented by this tree diagram?

• 3 shirt options, 6 pants options, and 12 shoe options

• 3 shirt options, 2 pants options, and 2 shoe options

• 2 shirt options, 3 pants options, and 1 shoe option

How many styles of sneakers are possible if Jared can choose from high-top or low-top, shoelaces or velcro, and the colors black, white, and red?

• 12

• 7

• 223

• 64

Shoppers in a large shopping mall are categorizes as male or female, over 40 or under 40, and cash or credit card shoppers. In how many ways can shoppers be categorized?

• 160

• 6

• 8

• 16

What is the total number of outcomes for picking a cat or dog and choosing the colors black, brown or spotted?

• 2

• 4

• 6

• 8