Analyzing Numerical Data Counting Principles

A seven-question quiz has 4 true/false questions followed by 3 multiple choice questions. For each multiple choice question there are four possible answers. In how many different ways is it possible to answer the seven questions?

• 12

• 80

• 28

• 1024

Sarah plays softball over the summer. If there are 10 players on the team, how many ways can the coach make a batting order that includes all players?

• 1

• 3628800

• 100

• 1814400

Brianna’s school day consists of six classes. How many different ways can her schedule be arranged?

• 720

• 36

• 100

• 500

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

Three students are scheduled to give oral reports on Monday. In how many ways can their presentations be ordered?

• 3 x 2 x 1 = 6

• 3 x 3 x 3 = 27

• 3 + 3 + 3 = 9

• 3 + 2 + 1 = 6

In how many ways can the first five letters of the alphabet be arranged if each letter is used only once?

• 5 x 4 x 3 x 2 x 1 = 120

• 5 x 5 x 5 x 5 x 5 = 3125

• 26 x 26 x 26 x 26 x 26 = 11881376

• 5 + 5 + 5 + 5 + 5 = 25

In how many different ways can 4 different books be arranged on the shelf?

• 4 x 3 x 2 x 1 = 24

• 4 x 4 x 4 x 4 = 256

• 4 + 3 + 2 + 1 = 10

• 4 + 4 + 4 + 4 = 16

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 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 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