Page 770 - Algebra 1

SOLUTION
Determine the number of ways each event can occur and then find their product.
4 types of toppings × 3 types of crust = 12 possible pizza combinations Check Use a tree diagram to verify that there are 12 possible pizza
combinations.
Mushrooms
Onions
Topping
Pepperoni
Thin Sausage Thick
Crust
Outcomes
Pepperoni Thin Pepperoni Thick
Thin
Thick
Traditional Pepperoni Traditional
Sausage Thin
Sausage Thick Traditional Sausage Traditional
Thin
Thick
Traditional Mushroom Traditional
Mushroom Thin Mushroom Thick
Thin
Thick
Traditional Onion Traditional
Onion Thin Onion Thick
Factorial
The factorial n! is defined for any natural number n as n! = n(n - 1)...(2)(1). Zero factorial is defined to be 1. 0! = 1.
Example: 5! = 5 · 4 · 3 · 2 · 1
Reading Math
The expression 8! is read “eight factorial.”
1st
2nd
3rd ...
6 Students
5 Students
4 Students
Online Connection www.SaxonMathResources.com
The tree diagram verifies that there are 12 possible outcomes.
When a group of people or objects are arranged in a certain order, the arrangement is called a permutation. The unique ways that 5 different colored blocks can be arranged are examples of permutations.
The factorial operation can be used to find different ways to arrange a set
of n different items, where the first item may be selected n different ways, the second item may be selected n - 1 ways, and so on.
There are n! ways to position n students in a line. For example, the number of ways 6 students can be positioned in a line can be described by 6!. As each position in the line is filled, the number of students that can be chosen to fill each position decreases by 1.
Notice only 5 students can be chosen for the 2nd position because 1 student has already filled the 1st position. Continuing this pattern shows that 6 students can be arranged in order 6!, or 6 · 5 · 4 · 3 · 2 · 1 = 720, different ways.
Lesson 111 755