Suppose you are in a small restaurant and are ready to order a soup, a main course, and a beverage. (Unfortunately, you will need to go somewhere else.

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Presentation transcript:

Suppose you are in a small restaurant and are ready to order a soup, a main course, and a beverage. (Unfortunately, you will need to go somewhere else for dessert!) The restaurant has 2 different soups, 3 different main courses, and 5 different beverages. If a meal consists of one item from each of the three categories, how many different meals are possible?

2x3x5 = 30 ways to select one item from each of the three categories.

Counting Methods – Part 1 Use basic counting methods to determine the number of ways of getting a sequence of events.

Practical Situations 1.Selecting a batting order for a team of baseball players 2.Selecting a set of courses to take at a college 3.Selecting a soup, dessert, and beverage when having dinner at a restaurant

Let’s visit a better restaurant!!! Suppose this restaurant has 4 different soups, 12 different main courses, 10 different desserts, and 8 different beverages. (Of course, you will have the opportunity to select a dessert after finishing the main course!) If a meal consists of one item from each of the four different categories, how many different meals are possible? 4x12x10x8 = 3840

Factorial! 5! Read as “five factorial” 5 x 4 x 3 x 2 x 1 = 120 The product involves starting with a positive integer and multiplying by each decreasing consecutive integer, until reaching the number 1. Factorials are not defined for fractions or decimals.

What is 0!? 0! is 1

Six people are to be assigned to 6 different seats. In how many ways can this be done? Seats Choices ! = 720 To enter 6! on calculator: MATH Arrow right to PRB Choose 4

Ten people wish to line up for a photograph. How many different arrangements are possible? 10! = 3,628,800 different arrangements

A high school bowling club consists of 8 members. A president, vice president and a treasurer are to be chosen. If 3 different people will be selected, in how many ways can this be done? Since there are only 3 available positions: 8(7)(6)=336 ways can be done

4! What is another way to express 4!?

Properties of factorials: Factorials cannot be used for decimals, fractions or any negative numbers.

Properties of factorials: The product of two factorial numbers is not equal to the factorial of their product or any arithmetic operation.

Properties of factorials: If n is any positive integer, then n! x(n+1)=(n+1)!