Lesson 29 : Multiplication Counting Principle

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CHOICES, CHOICES, CHOICES

• Lesson 2-9 Multiplication Counting Principle

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MEET THE GANG
(Click on their picture to see how they can help
you.)
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Angelica
TADAA!

• Youll see Angelica when you get the right answer
  and are ready to move on.

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Tommy
Im excited to teach you about todays lesson. I
will appear when instructions or assignments will
be given.
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Spike
Oh, thats RUFF!

• If you see Spike, youve made a mistake, and must
  try again.

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Kira
If you need help or step by step suggestions
click on me.
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What is the Multiplication Counting Principle?
If one choice can be made in m ways and a second
choice can be made in n ways, then there are mn
ways of making the first choice followed by the
second choice. Lets look at a few example
problems.
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Example 1

• ProblemThe stadium at the left has 9 gates to
  enter and exit the building. Gates A, B, C, and
  D on the north side, and Gates E, F, G, H, and I
  on the south.
• QuestionIn how many ways can you enter the
  stadium through a north gate and leave through a
  south gate?

Kiras here to help.
A B C D
E F G H I
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Answer Ex.1
(Click here to see the problem again.)
Q. In how many ways can you enter the stadium
through a north gate and leave through a south
gate?

• 9 ways

B. 20 ways
C. 12 ways
D. 1 way
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Create an array
Creating an array will map out your possibilities
in an organized way. Now you can either count
the possibilities or multiply the number of rows
by the number of columns.
MOREHELP
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What about this?
I wonderHow many ways could you enter (4)? And
how many ways could you have exited (5)? 4 ? 5
___ ways. THATS the Multiplication Counting
Principle.
ANSWER
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Oh, thats RUFF
See Kira
Not Quite.Kira will review problem with you,
then give you the chance to try again.
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Ta-daaa!
Youre Correct! You may now move on to the next
problem. Keep up the good work!
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Example 2
Band or Choir??
French, Spanish, or German?
Kiras here to help.
Drawing or Painting???

• ProblemA student wants to take a foreign
  language (French, Spanish, or German), a music
  (band or choir), and an art (drawing or painting)
  class this year.
• QuestionIn how many different ways can this
  student choose three classes?

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Create an organized list
Creating an organized list (like an array). It
will help you avoid repeating combinations. Now
you can count the number of combinations you
created.
MOREHELP
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orCreate a Tree Diagram
drawing painting drawing painting drawing painti
ng drawing painting drawing painting drawing pa
inting
choir band choir band choir band
French Spanish German
A tree diagram will require less writing and keep
you just as organized. Now you can count number
of paths to the end.
MOREHELP
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What about this?
Rememberthe Multiplication Counting Principle?
Take the choices for foreign language (3), times
choices for music (2), times choices for art (2).
Mathematically that leaves you with 3 ? 2 ?
2 ____ ways
ANSWER
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Answer Ex. 2
(Click here to see the problem again.)
Q. In how many different ways can this student
choose three classes?

• 21 ways

B. 7 ways
C. 3 ways
D. 12 ways
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Oh, thats RUFF
See Kira
Try Again.See Kira for review, then you will
get another chance.
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Ta-daaa!
Perfect! You may now move on to the next
problem. Youre starting to really get it!
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Example 3
Kiras here to help.

• ProblemMr. Smith is giving his math class a
  pop quiz with five questions. Ann hasnt studied
  so she must guess. The quiz has three multiple
  choice and two true-false questions.
• QuestionHow many ways are there to answer the
  quiz?

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Multiplication Counting Principle
POP QUIZ 1. Multiple Choice (A, B, C, D) 4
choices 2. Multiple Choice (A, B, C, D) 4
choices 3. Multiple Choice (A, B, C, D) 4
choices 4. True/False 2 choices 5. True/False
2 choices So.. think 1. 4 choices 2. 4
choices 3. 4 choices 4. 2 choices 5. 2
choices Using the Multiplication Counting
Principle 4 ? 4 ? 4 ? 2 ? 2
____ ways
Other methods would get confusing and difficult
to organize. Think about your choices.
Answer
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Answer Ex. 3
(Click here to see the problem again)
Q. How many ways are there to answer the quiz?

• 128 ways

B. 114 ways
C. 24 ways
D. 40 ways
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Oh, thats RUFF
See Kira
Nope.Try again after your appointment with Kira.
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Ta-daaa!
Amazing! You have completed the lesson and ready
for your assignment. Tommy will give you the
numbers assigned for today! Super Job!
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Todays Assignment
I see youve completed the lesson. Way to go!
Angelica said you have done very well and are
ready for todays assignment.
Do these problems for tomorrow Covering the
Reading(p. 122) 1-9
STARTOVER