Page 769 - Algebra 1

L E S S O N Solving Problems Involving Permutations 111
Warm Up
1. Vocabulary (Experimental, Theoretical ) probability is found
(14)
2. What is the probability of rolling a number greater than 3 on a number
(14)
cube labeled 1–6?
3. What is the probability of rolling a number greater than 7 on a number
(14)
Identify each set of events as independent or dependent. 4. Rolling a 5 on one number cube and a 3 on another.
(33)
5. Drawing a blue marble from a bag, keeping it, and then drawing a red
(33)
marble.
by analyzing a situation and finding the ratio of favorable outcomes to all possible outcomes.
cube labeled 1–6?
New Concepts
A tree diagram can be used to determine the number of ways 2 pairs of pants and 4 shirts can be arranged to make different outfits. However, the number of possible outcomes can be determined by multiplying the number of ways the first event can occur by the number of ways the second event can occur.
first event second event total possible outcomes 2 pairs of pants × 4 shirts = 8 outfits
This method is an application of the Fundamental Counting Principle. The Fundamental Counting Principle can be used to determine the number of possible outcomes in situations involving independent events.
Fundamental Counting Principle
If an independent event M can occur in m ways and another independent event N can occur in n ways, then the number of ways that both events can occur is
m · n.
Example: A restaurant offers 4 entrées and 5 vegetable dishes. How many
meals with one entrée and one vegetable dish are possible? 20 meals may be ordered since 4 · 5 = 20.
Example
1
Using the Fundamental Counting Principle
A 1-topping pizza can be ordered with a choice of 4 different toppings: pepperoni, sausage, mushrooms, or onion. There is also a choice of different types of crust: thin, thick, or traditional. Find the number of ways that a 1-topping pizza can be ordered using the Fundamental Counting Principle.
Math Reasoning
Predict How many different pizzas would be possible if you had 5 choices for toppings and 2 choices for crust?
754 Saxon Algebra 1