11-6 Combinations Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation...
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Transcript of 11-6 Combinations Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation...
11-6 Combinations
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Mrs. Logan’s class has to read any two of the following books.
1. The Adventures of Tom Sawyer, by Mark Twain2. The Call of the Wild, by Jack London3. A Christmas Carol, by Charles Dickens
4. Treasure Island, by Robert Louis Stevenson
5. Tuck Everlasting, by Natalie Babbit
How many possible combinations of books could the students choose?
Course 2
11-6 Combinations
A combination is a grouping of objects or events in which the order does not matter. For example, a student can choose books 1 and 2 or books 2 and 1. Since the order does not matter, the two arrangements represent the same combination. One way to find possible combinations is to make a table.
Course 2
11-6 Combinations
Additional Example 1: Using a Table to Find Combinations
Kristy’s Diner offers customers a choice of 4 side dishes with each order: carrots, corn, french fries, and mashed potatoes. How many different combinations of 3 side dishes can Kareem choose?
Begin by making a table showing all the possible choices of side dishes taken three at a time.
1, 2, 3 2, 1, 3 3, 1, 2 4, 1, 2
1, 2, 4 2, 1, 4 3, 1, 4 4, 1, 3
1, 3, 4 2, 3, 4 3, 2, 4 4, 2, 3Course 2
11-6 Combinations
Because order does not matter, you can eliminate repeated triples. For example 1, 2, 3 is already listed, so 2, 1, 3 can be eliminated.
Additional Example 1 Continued
1, 2, 3 2, 1, 3 3, 1, 2 4, 1, 2
1, 2, 4 2, 1, 4 3, 1, 4 4, 1, 3
1, 3, 4 2, 3, 4 3, 2, 4 4, 2, 3
There are 4 possible combinations of 3 side dishesKareem can choose with his order.
Course 2
11-6 Combinations
Check It Out: Example 1
Insert Lesson Title Here
Jim is packing for a trip. He has 4 different colors of shirts: red, green, blue, and yellow(r, g, b, y). He only has room for 3 of them. How many different combinations of 3 shirts can Jim choose for his trip?
Begin by making a table of all the possible choices of shirts taken three at a time.
r, g, b g, r, b b, r, g y, r, g
r, g, y g, r, y b, r, y y, r, b
r, b, y g, b, y b, g, y y, g, b
Course 2
11-6 Combinations
Check It Out: Example 1 Continued
Insert Lesson Title Here
Because order does not matter, you can eliminate repeated triples. For example r, g, b is already listed so g, r, b can be eliminated.
There are 4 possible combinations of 3 shirtsthat Jim can choose to bring on his trip.
r, g, b g, r, b b, r, g y, r, g
r, g, y g, r, y b, r, y y, r, b
r, b, y g, b, y b, g, y y, g, b
Course 2
11-6 Combinations
Lara is going to make a double-dip cone from a choice of vanilla, chocolate, and strawberry. She wants each dip to be a different flavor. How many different cone combinations can she choose from?
Additional Example 2: Problem Solving Application
11 Understand the Problem
Rewrite the question as a statement.• Find the number of possible combinations of
two flavors Lara can choose.
List the important information:
• There are three flavor choices in all.
Course 2
11-6 Combinations
Additional Example 2 Continued
22 Make a Plan
You can make a tree diagram to show thepossible combinations.
Course 2
11-6 Combinations
Additional Example 2 Continued
Solve33
VanillaChocolate
StrawberryChocolate
Vanilla
Strawberry
StrawberryChocolate
Vanilla
The tree diagram shows 6 possible ways to combine two flavors, but each combination is listed twice. So there are 6 ÷ 2 = 3 possible combinations.
Course 2
11-6 Combinations
Look Back44
You can also check by making a table. The vanilla can be paired with two other flavors and the chocolate with one. The total number of possiblepairs is 2 + 1 = 3.
Additional Example 2 Continued
Course 2
11-6 Combinations
Check It Out: Example 2
Insert Lesson Title Here
Hamilton had three flavors of cookies: sugar, chocolate chip, and oatmeal. He wants to put them into packages, with each package containing two different flavors of cookies. How many different packages can he make?
11 Understand the Problem
Rewrite the question as a statement.
• Find the number of possible combinations that Hamilton can choose.List the important information:
• There are three cookie types in all.
Course 2
11-6 Combinations
Check It Out: Example 2 Continued
Insert Lesson Title Here
22 Make a Plan
You can make a tree diagram to show thepossible combinations.
Course 2
11-6 Combinations
Check It Out: Example 2 Continued
Insert Lesson Title Here
Solve33
OatmealChocolate chip
SugarSugar
Chocolate chip
Oatmeal
Chocolate chipOatmeal
Sugar
The tree diagram shows 6 possible ways to combinetwo flavors, but each combination is listed twice. So there are 6 ÷ 2 = 3 possible combinations.
Course 2
11-6 Combinations