10. Sequences, Induction, and Probability

In Exercises 1–8, use the formula for nPr to evaluate each expression. 9P4

In Exercises 1–8, use the formula for nPr to evaluate each expression. 7P3

In Exercises 1–8, use the formula for nPr to evaluate each expression. 8P5

In Exercises 1–8, use the formula for nPr to evaluate each expression. 10P4

In Exercises 1–8, use the formula for nPr to evaluate each expression. 9P9

In Exercises 1–8, use the formula for nPr to evaluate each expression. 8P0

In Exercises 9–16, use the formula for nCr to evaluate each expression. 9C5

In Exercises 9–16, use the formula for nCr to evaluate each expression. 10C6

In Exercises 9–16, use the formula for nCr to evaluate each expression. 11C4

In Exercises 9–16, use the formula for nCr to evaluate each expression. 4C4

In Exercises 9–16, use the formula for nCr to evaluate each expression. 5C0

In Exercises 9–16, use the formula for nCr to evaluate each expression. 6C0

In Exercises 21–28, evaluate each expression.

In Exercises 21–28, evaluate each expression.

In Exercises 21–28, evaluate each expression.

Use the Fundamental Counting Principle to solve Exercises 29–40. A popular brand of pen is available in three colors (red, green, or blue) and four writing tips (bold, medium, fine, or micro). How many different choices of pens do you have with this brand?

Use the Fundamental Counting Principle to solve Exercises 29–40. An ice cream store sells two drinks (sodas or milk shakes) in four sizes (small, medium, large, or jumbo) and five flavors (vanilla, strawberry, chocolate, coffee, or pistachio). In how many ways can a customer order a drink?

Use the formula for nCr to solve Exercises 49–56. Of 12 possible books, you plan to take 4 with you on vacation. How many different collections of 4 books can you take?

Use the formula for nCr to solve Exercises 49–56. You volunteer to help drive children at a charity event to the zoo, but you can fit only 8 of the 17 children present in your van. How many different groups of 8 children can you drive?

Evaluate the expression. *permutation notation* the number of permutations 8 things taken 3 at a time (sub 8)P(sub 3)

A club with 15 members is to choose four officers–president, vice president, secretary, and treasurer. In how many ways can these offices be filled?

How many different ways can a director select 4 actors from a group of 20 actors to attend a workshop on performing in rock musicals?

How many four-digit odd numbers less than 6000 can be formed using the digits 2, 4, 6, 7, 8, and 9?

In Exercises 1–8, use the formula for nPr to evaluate each expression. 6P6

In Exercises 9–16, use the formula for nCr to evaluate each expression. 7C7

In Exercises 21–28, evaluate each expression.

Use the Fundamental Counting Principle to solve Exercises 29–40. The model of the car you are thinking of buying is available in nine different colors and three different styles (hatchback, sedan, or sport). In how many ways can you order the car?

Use the formula for nCr to solve Exercises 49–56. An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

Use the formula for nCr to solve Exercises 49–56. To win at LOTTO in the state of Florida, one must correctly select 6 numbers from a collection of 53 numbers (1 through 53). The order in which the selection is made does not matter. How many different selections are possible?

Evaluate the expression. *permutation notation* the number of permutations 9 things taken 5 at a time (sub 9)P(sub 5)

In how many ways can five airplanes line up for departure on a runway?

In Exercises 1–8, use the formula for nPr to evaluate each expression. 6P6

In Exercises 9–16, use the formula for nCr to evaluate each expression. 7C7

In Exercises 21–28, evaluate each expression.

Use the Fundamental Counting Principle to solve Exercises 29–40. The model of the car you are thinking of buying is available in nine different colors and three different styles (hatchback, sedan, or sport). In how many ways can you order the car?

Use the formula for nCr to solve Exercises 49–56. An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

Use the formula for nCr to solve Exercises 49–56. To win at LOTTO in the state of Florida, one must correctly select 6 numbers from a collection of 53 numbers (1 through 53). The order in which the selection is made does not matter. How many different selections are possible?

Evaluate the expression. *permutation notation* the number of permutations 9 things taken 5 at a time (sub 9)P(sub 5)

In how many ways can five airplanes line up for departure on a runway?