Contemporary Mathematics Topic 18 The Sequential Counting Principle

Contemporary Mathematics Topic 18: The Sequential Counting Principle

Tree Diagrams › Tree diagrams can be used in relatively small cases to count the number of outcomes. › Suppose you have a True/False test with 3 questions – how many answer possibilities are there? › You can use a tree diagram to map out these different choices.

Example 1: › Use a tree diagram to find out how many outcomes are possible. › A) Flipping 2 coins. › B) Picking a Red or Blue shirt and a Blue, Beige, or Black pair of pants. › C) Picking between 3 menu items and 5 drink choices.

The Sequential Counting Principle › If one event can happen in m ways and a second event can happen in n ways, the sequence of events (as long as they are independent) can occur in m X n ways. › For example, if a hospital offers on its patient menu 5 meals, 6 snacks, and 3 desserts, there would be 5 x 6 x 3 = 90 different ways to choose a choice.

Example 2: › If the mall has 3 stores down one hallway, 5 stores down the second hallway, and 7 stores down a third hallway, how many different ways can one store from each hallway be chosen? › A mail delivery center gives each of its 8 drivers 6 bins each of mail to deliver, and each bin has 300 letters. How many letters are being delivered?

Example 3: › A chain email begins with 1 person sending out 6 emails. Each recipient then sends out 6 emails. Each of those recipients then sends out 6 emails. How many total emails were sent? › In 1995, new restrictions were put on phone numbers in the U. S. The area code could not begin with a 0 or a 1. In addition, the 7 -digit primary number cannot begin with a 0 or a 1. How many 10 -digit U. S. phone numbers are possible?

Example 4: › A slot machine’s possibilities is shown below: Symbol Line 1 Line 2 Line 3 Lucky 7 1 1 1 Bar 3 2 1 Cherry 7 3 5 Bell 3 3 3 Lemon 4 6 5 Orange 2 5 5 › How many symbol arrangements are possible? › How many ways can you get triple 7’s? Triple Bar?