Counting Rules and Probability

Two fair dice are rolled, determine the probability that the sum of the two dice is 11.

• 2/12

• 2/36

• 11/36

• 11/12

If the letters A, B, C, D, E, and F are to be used in a five-letter code, how many different codes are possible if repetitions are not permitted?

• 625

• 720

• 7776

• 1296

A store manager wants to display 4 different brands of toothpaste in a row. How many ways can this be done?

• 4

• 12

• 6

• 24

There are __________ possible ways that eight pictures can be hung along a wall.

• 18316

• 23596

• 40320

• 1648

When a die is rolled twice, there are __________ possible outcomes.

• 8

• 18

• 36

• 48

Evaluate the following: ₇P₃.

• 210

• 35

• 5040

• 6

The number of different arrangements of four pictures from a selection of ten pictures is 5,040

• True

• False

A business has seven locations to choose from and wishes to rank only the top three locations. How many different ways can this be done?

• 5040

• 210

• 840

• 420

There are 3 different mathematics courses, 5 different science courses, and 2 different history courses. If a student must take one of each, how many different ways can this be done?

• 10

• 12

• 30

• 60

Evaluate the following: ₇C₃

• 210

• 5040

• 35

• 6