9. Sequences, Induction, and Probability

Use the Fundamental Counting Principle

Counting Principles, Permutations, and Combinations

Multiplication Principle - Counting Techniques

In Exercises 21–28, evaluate each expression.

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?

Permutations Involving Repeated Symbols - Example 2

Fundamental Counting Principle

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?

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

9P4

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.

8P5

Theoretical Probability, Permutations and Combinations

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

7C7

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?

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?

Permutations Made Easy- Counting Using Permutations

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?

Probability: The Counting Principle

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

11C4

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

8P0

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?

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

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?

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?

What Is And How Does The Fundamental Counting Rule Principle Work In Probability Statistics Math

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?

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

5C0

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

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

Permutations Involving Repeated Symbols - Example 1

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Find the Common Difference for an Arithmetic Sequence

Write Terms of an Arithmetic Sequence

Use the Formula for the General Term of an Arithmetic Sequence

Use the Formula for the Sum of the First <i>n</i> Terms of an Arithmetic Sequence

Arithmetic Sequences

Compute Empirical Probability

Compute Theoretical Probability

Find the Probability that an Event will Not Occur

Find the Probability of One Event or a Second Event Occurring

Find the Probability of One Event and a Second Event Occurring

Probability

Evaluate a Binomial Coefficient

Expand a Binomial Raised to a Power

The Binomial Theorem

Distinguish Between Permutation and Combination Problems

Use the Permutations Formula

Find Particular Terms of a Sequence from the General Term

Use Recursion Formulas

Use Factorial Notation

Use Summation Notation

Sequences and Summation Notation

Understand the Principle of Mathematical Induction

Prove Statements Using Mathematical Induction

Mathematical Induction

Find the Common Ratio of a Geometric Sequence

Write Terms of a Geometric Sequence

Use the Formula for the General Term of a Geometric Sequence

Use the Formula for the Sum of the First <i>n</i> Terms of a Geometric Sequence

Find the Value of an Annuity

Use the Formula for the Sum of an Infinite Geometric Series

Geometric Sequences and Series

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