Section 0-4 Counting Techniques

Find the total number of outcomes using a variety of methods. Objective

A bicycle manufacturer makes five- and ten-speed bikes in seven different colors and four different frame sizes. How many different bicycles does the manufacturer make? Example 1

You are buying a pizza. You have a choice of 3 crusts, 4 cheeses, 5 meat toppings, and 8 vegetable toppings. How many different pizzas with one crust, one cheese, one meat, and one vegetable can you choose? Example 1

A permutation is a rearrangement of items in a group of items in which the ORDER that the items occur MATTERS. A rearrangement is considered to be different if the ORDER in which the items occur is different. Vocabulary

There are 9 finalists in a band competition There are 9 finalists in a band competition. In how many different ways can the bands be ranked if they cannot receive the same ranking? Example 2

Eight teams are competing in a baseball playoff Eight teams are competing in a baseball playoff. In how many different ways can the baseball teams finish the competition? Example 2

How many different ways can two students be assigned to five tutors if only one students is assigned to each tutor? Example 3

You have 6 homework assignments to complete over the weekend You have 6 homework assignments to complete over the weekend. However, you only have time to complete 4 of them on Saturday. In how many orders can you complete 4 of the assignments? Example 3

A television news director has 9 news stories to present on the evening news. a) How many different ways can the stories be presented? b) If only 3 of the stories will be presented, how many possible ways can a lead story, a second story, and a closing story be presented? Example 3

The standard configuration for a license plate is 3 letters followed by 4 numbers. a) How many different license plates are possible if letters and digits can be repeated? b) How many different license plates are possible if letters and digits cannot be repeated? Example 3

Vocabulary ♠ ♣ ♥ ♦ ♥ ♦ ♠ ♣ ♠ ♥ ♣ ♦ A combination is a rearrangement of items in a group of items in which the ORDER that the items occur does NOT matter. ♠ ♣ ♥ ♦ ♥ ♦ ♠ ♣ ♠ ♥ ♣ ♦ All three of the above groups are considered to be the same combination of the four items in the group since all that is different is the order of the items. Vocabulary

How many ways are there to choose 5 cards from a standard deck of 52 playing cards? Example 4

You are picking 7 books from a stack of 32 You are picking 7 books from a stack of 32. If the order of the books you choose is not important, how many different 7 book groups are possible? Example 4

Twenty-five students write their names on slips of paper Twenty-five students write their names on slips of paper. Then three different names are chosen at random to review prizes. a) How many different way can you choose 3 people to each receive a “no homework” coupon. b) How many different ways can you choose 3 people to each receive one of the following prizes: 1st chosen: a new graphing calculator, 2nd chosen: a “no homework” coupon; 3rd chosen: a new pencil. Example 4

Determine if the following would use a permutation or a combination: A president, vice-president, and secretary are chosen from 25- member club A cook chooses 5 potatoes from a bag of 12 potatoes for making potato salad 13 cards are selected from a deck of 52 to form a bridge hand 4 actors are chosen to play the Beatles in a film biography A teacher makes a seating chart for 22 students in a classroom with 30 desks 7 digits are selected to form a telephone number 4 students are selected from the senior class to form a committee to advise the cafeteria director about food Example 5

p.P12 #1 – 18 Homework