Permutations

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Permutations Combinations
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Counting Principle

• If there are 3 meats, 5 vegetables, and 2 types
  of bread to choose from for a meal, how many
  different meals are possible?

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How many answer keys are possible for a 5
question true/false quiz?
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How many 7-digit phone numbers are possible?
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If a license plate has 3 letters followed by 3
numbers, how many plates are possible?
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How many ways can I read six magazines out of 10?
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Permutation order is important

• Suppose that a club with 12 members wishes to
  choose a president, a vice-president, and a
  treasurer.
• The order is important.
• How many ways can this be done?

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Can you develop a formula for finding a
permutation?
Lets check to see if youre right
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Combination order doesnt matter

• Suppose the club merely wants to choose a
  governing council of 3.
• Now for each governing council of 3 that can be
  chosen (say A, B, C) there are ____ different
  slates of officers. In other words they are the
  same.

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So how many governing councils are there?
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Can you develop a formula for Combinations?
Lets check to see if youre right!
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I want to take three books out of my collection
of 10 to school to put on my desk. How many ways
can this be done?
13
A company advertises two job openings for
computer programmers, both with the same salary
and job description. In how many ways can the
openings be filled if 8 people apply?
14
A company advertises two job openings, one for a
copywriter and one for an artist. If 10 people
who are qualified for either position apply, in
how many ways can the openings be filled?
15
For a certain raffle, 845 tickets are sold. In
how many ways can four 50 gift certificates be
awarded?
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How many ways can a 100, a 50, a 20, and a 10
gift certificate be awarded?
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Permutations Combinations can be done on the
graphing calculator!

• Type the n ( of items)
• Press math, Prb
• Choose the appropriate key (2 or 3)
• Type the r ( chosen)
• Press enter

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How many ways can I choose six people for a
committee in a class of 20?
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How many ways can I select four bikes from seven?
20
At the Red Lion Diner, an omelet can be ordered
plain or with any or all of the following
fillings cheese, onions, peppers. How many
different kinds of omelets are possible?
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There are 8 different kinds of cookies and 11
different cakes. How many ways can I choose 3
types of cookies and 5 different cakes?
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There are 10 different magazines and 12
different books. How many ways can I choose 3 if
I want at most 2 books?
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How many permutations are in the word letter?
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How many permutations are in the word Mississippi?
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Homework

• Worksheet