1. 8.2 Notes.notebook December 20, 2012
8.2 Permutations
A permutation of a set of objects is:
An arrangement of objects where they are placed in a
distinct ORDER.
This fact is very important since we will find out that if
order does NOT matter then we do NOT have a
permutation.
The questions we did in 8.1 were permutation
questions, since when we arrange letters, or digits,
or place people in a row, then every arrangement is
different.
May 2­5:45 PM
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2. 8.2 Notes.notebook December 20, 2012
How many ways can we arrange 5 people into a row of 3.
_____, _______,______ is how we did this question using
the fundamental counting principle.
Now we will derive a permutation formula to get the same result.
P
5 3 means 5 objects taken 3 at a time, and the result is:
=__________
Notice the result is the same!
May 2­7:02 PM
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3. 8.2 Notes.notebook December 20, 2012
In general, if n objects are taken r at a time, then the number
of permutations is:
P =
n r
Ex's)
a) arrangements of the word "solid"
b) 2 letters arrangements from the word "solid"
Notice we can use the formula or we can fill in the appropriate
number of blanks and use the fundamental counting principle.
May 2­7:07 PM
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4. 8.2 Notes.notebook December 20, 2012
Many permutation arrangement questions do NOT
require the formula. Think about the restrictions!
Ex) How many ways can 4 boys and 4 girls sit in a row if:
a) the boys and girls must alternate?
b) a boy must sit at each end?
May 2­7:12 PM
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5. 8.2 Notes.notebook December 20, 2012
Last class we looked at repetition of identical objects.
A DIFFERENT version of arrangements occurs when objects
are grouped together.
Ex)
a) How many ways can 5 people be arranged on a bench?
b) If 2 of them must sit together?
c) If 2 couples must sit together?
d) if 2 of them must NOT sit together?
May 2­7:14 PM
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6. 8.2 Notes.notebook December 20, 2012
How many ways can 3 different social studies textbooks,
4 math texts , 3 science texts and 2 French texts
be arranged on a shelf if the books must stay together by subject?
b) If there must be a French text at each end of the shelf?
May 3­8:29 AM
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7. 8.2 Notes.notebook December 20, 2012
Sometimes we must use the permutation formula
to solve questions.
Ex) Solve nP2 = 30
Ex) Solve 6Pr = 30
May 3­8:31 AM
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8. 8.2 Notes.notebook December 20, 2012
Homework: Pg. 701
#3, 4, 5(ignore graphic organizer!)
6a)b), 7, 8, 10, 11, 12a) Mult. Ch #1,2,3
Page 712
#3,5, 6i)iii),7,8,,9,12 Mult Ch. #1,2
May 3­8:34 AM
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