Counting Principles

A cube, with faces numbered 1 to 6, is rolled, and a penny is tossed at the same time. How many elements in the sample space consist of an even number and a tail?

• 12

• 2

• 3

• 4

When a fair coin was tossed ten times, it landed heads up the first seven times. What is the probability that on the eighth toss the coin will land with tails up?

Tags

CCSS.HSS.CP.A.5

Maria has a set of 10 index cards labeled with the digits 0 through 9. She puts them in a bag and selects one at random. The outcome that is most likely to occur is selecting.

• an off number

• a prime number

• a number that is at most 5

• a number that is divisible by 3.

Five students, Caroline, Ashley, Malika, Gianna, and Lily, line up one behind the other. How many different ways can they stand in line?

• 60

• 5

• 25

• 120

How many different three-member teams can be selected from a group of seven students?

• 35

• 1

• 210

• 5040

₇P₂

• 0
• 7
• 42
• 210

Permutation, combination, or neither?
The batting order for seven players on a 12 person team.

• combination
• permutation
• neither

₁₂C₃

• 36
• 66
• 220
• 500

24 students are in the Geometry class. Every week the class is rearranged into groups of 3. What is the probability that John will be grouped with his 2 friends, Nate and Jack?

• 1/72

• 1/4048

• 1/2024

• 3/12144

Tags

CCSS.HSS.CP.B.9

How many ways can a club select a president, vice president, and a secretary from a group of 5 people?

• 12

• 60

• 15

• 125