Counting Rules and Probability

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

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?

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

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

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

Evaluate the following: ₇P₃.

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

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?

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?

Evaluate the following: ₇C₃