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1 14.1 (B.16) Counting Outcomes.notebook
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May 27, 2014
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WarmUpSimplify
1. 2.
3.
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Today’s Agenda• WarmUp
• 14.1 Counting Outcomes
• B.16 – Counting principles, permutations, and combinations
• Classwork
• Homework
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14.1 Counting OutcomesGoals:
• Count outcomes using a tree diagram.• Count outcomes using the Fundamental Counting Principle.
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Tree Diagrams• Tree Diagram – a method used for counting the number of possible outcomes
• Sample Space – the list of all possible outcomes
• Event – a collection of one or more outcomes in the sample space.
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A football team uses red or gray jerseys. They use gray or black pants, and black or white shoes. Use a tree diagram to determine the number of outfits you can create.
Example #1
JERSEYS PANTS SHOES OUTCOMES
RED
GRAY
GRAY
BLACK
GRAY
BLACK
BLACKWHITEBLACKWHITEBLACKWHITEBLACKWHITE
RGBRGWRBBRBWGGBGGWGBBGBW
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• Create a tree diagram to represent the outcomes of tossing a coin three times.
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Example #3• Suppose you need to create a three digit code from the numbers 1 – 4. If you cannot repeat a number, create a tree diagram representing the outcomes.
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Fundamental Counting Principle
• FCP – If one event can occur in m ways and is followed by another event that can occur in n ways, then the amount of total outcomes can be calculated by m · n.
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Example #4A deli offers a lunch special in which you can choose a sandwich, a side dish, and a beverage.
If there are 10 different sandwiches, 12 different side dishes, and 7 different beverages, how many different specials can you order? (Use FCP!)
sandwich side dish beverage
· ·
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Examples #5 – 6 In your closet, you have 8 pairs of jeans, 15 shirts, and 3 jackets. How many different outfits can you make?
When purchasing a new car, you must choose from 4 different interior colors, 6 different exterior colors, and 3 different styles. How many different types of designs can you choose from?
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Factorial• The expression n! (read n factorial), where n is greater than zero, is the product of all positive integers beginning with n and counting backward to 1.
• n! = n · (n – 1) · (n – 2) · … · 3 · 2 · 1
• 5! = 5 · 4 · 3 · 2 · 1 = 120
• 7! =
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Examples #7 – 9 • 6!
• (10 – 2)!
• Emily cannot decide in which order to ride the 12 roller coasters in the park.
• How many different orders can she ride all of the roller coasters?
• If she only has time to ride 8 of the roller coasters, how many ways can she do this?
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Classwork• 14.1 Counting Outcomes
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What STUCK with You?
• Topic – Fundamental Counting Principle
• Create and solve your own problem using BOTH the Fundamental Counting Principle AND a tree diagram.
• You must use AT LEAST 3 events!
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Almost Finished...
Take out your agenda copy down due datesStandard Checks
Homework14.1 Counting Outcomes
Do NOT pack up until you are told to do so!
Tests
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Homework
• 14.1 Practice