Name __________________________
TPC out of Blue and Gold Book - Section 6-7 (p345-351) Modified
Part 1 EQ: How do we determine all possible outcomes of an event?
Part 2 EQ: How are the number of arrangements of objects in a set calculated?
Warm up:
I. Multiplication Counting Principle
Example A
Suppose a stadium has 9 gates as shown above. Gates A, B, C, and D are on the north side.
Gates E, F, G, H, and I are on the south side.
In how many ways can you enter the stadium through a north gate and leave through a south
gate?
Multiplication Counting Principle
If there are m ways to make one choice and n ways to make a second choice, then there are
______ ways to make the first choice followed by the second choice.
Name __________________________
Example B
A high-school student wants to take a foreign-language class, a music course, and an art
course. The language classes available are French, Spanish, and German. The music classes
available are chorus and band. The art classes available are drawing and painting. In how
many different ways can the student choose the three classes?
Example C
Mr. Lorio is giving his algebra class a quiz with five questions. Since Angie has not done her
homework, she has to guess. The quiz has two multiple-choice questions with choices A, B, C,
and D, and three true-false questions.
a. How many possible ways are there for Angie to answer all five questions?
b. What is the probability that Angie will get all the questions correct?
Example D
Ms. Alvarez has written a chapter test. It has three multiple-choice questions each with m
possible answers, two multiple-choice questions each with n possible answers, and 5 true-false
questions. How many ways are there to answer the questions?
Warm-up for next part:
List the ice flavors: Vanilla, Chocolate, Strawberry, and Cookies ‘n Cream in order of your most
favorite to least favorite.
Name __________________________
II. Permutations
Example 1 pg 345:
In how many orders can ten dogs line up to be groomed?
Example 2 pg 346
Name __________________________
Example 2B: Johnny has 7 math books to line up on a shelf. Jenny has 3 English books to line
up on a shelf. In how many more orders can Johnny line up his books than Jenny?
Permutations involving repetition (must divide by factorial number of each repeated item)
In how many orders can you arrange the letters of the word MISSISSIPPI?
III. Combinations
In example 2, the order that the yachts finish matters, but suppose instead you were picking a
committee of 3 people from a pool of 7 people. In this committee scenario, all members of
the committee have an equal rank so the order in which you pick the members does not
matter. A selection in which order does not matter is called a combination.
Example 3 pg 347
Evaluate 12C3.
Example 4 pg 347
Name __________________________
Example 5 pg 347
Example 6
Sue has a coupon for a free one-scoop ice cream cone, she may choose any of three types of
cones (kidde, sugar, or pretzel), any of six flavors (vanilla, chocolate, strawberry, mint
chocolate chip, cookies n cream, or butter pecan) and it may have one of three toppings
(peanuts, chocolate sauce or carmel).
a. How many ways could she choose an ice cream cone?
b. Determine how many more or less ways she could use the coupon if she were
allowed to choose two scoops instead of one.
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Name __________________________
HW: Pg 348