12.1 The Counting Principle

Vocabulary

Independent Events: choice of one thing DOES NOT affect the choice of another

Dependent Events: choice of one thing DOES affect the choice of another

Outcome: the result of a single trial

Sample Space: set of all possible outcomes

Event: one or more outcomes of a trial

The Fundamental Counting Principle

If one event can occur m ways and another event can occur in n ways, then one event followed by the other event can occur in mn ways

Basically multiply the number of ways for each event to get the total number of ways the events can occur together

Examples

A sandwich cart offers the choice of hamburger, chicken or fish on plain or sesame bun. How many combinations of meat and bun are possible? Note: meat choice does not affect bun

choice so these events are independent

An ice cream shop offers two types of cones or a bowl, 17 flavors of ice cream, and 40 toppings. How many combinations of one-scoop, one-topping sundaes can you order?

Kim won a contest on the radio. The prize was a restaurant gift certificate and tickets to a sporting event. She can select one of three restaurants and tickets for football, baseball, basketball, or hockey game. How many different ways can she select a restaurant followed by a sporting event?

The Murray’s are choosing a trip to the beach or the mountains. They can travel by car, train, or plane. How many ways can the family select a trip followed by means of transportation?

How many answering machine codes are possible if the code is two digits?

How many license plates can be made if the first three places must be letters and the last three must be numbers?

How many area codes are possible if each area code is 3-digits?

How many ATM pin numbers are there if each pin number is 4 characters long and each character could be a number or a letter?

Charlita wants to take 6 different classes next year. Assuming that each class is offered each period, how many different schedules could she have? Note if she takes Algebra II first period

she won’t take it another period… so this is a dependent event.

Each player in a board game uses one of six different pieces. If four players play the game, how many different ways could the players choose their game pieces?

An ice cream shop offers a choice of two types of cones and 15 flavors of ice cream, and the choice of peanuts, chocolate sprinkles, or crushed oreos for toppings. How many different 1-scoop, 1-topping cones can a customer order?