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Acc Math 1
EQ:What is the difference between a permutation and combination?
CombinationCombination
n is the total and r is the amount chosen
A selection of objects where order is NOT important.
On the CalculatorOn the Calculator
• n must be typed in first• Then, Math• PRB• CHOICE 3• Type in r• Enter
CombinationsCombinations
A selection of objects in which order is not important.
Example: Eight people pair up to do an assignment. How many different pairs are there?
Example 1
How many different ways are
there to select two class
representatives from a class of
20 students?
Example 2
From your class of 24, the teacher is randomly selecting 3 to help Mr. Shaw with a project. How many combinations are possible?
Example 3
For your school pictures, you can choose four backgrounds from a list of ten. How many combinations of backgrounds are possible?
Example 4
Coach Hill randomly selects 3 people out of his class of 20 to go to the courts and help him get ready for a tennis match. How many possibilities of people does he have?
Example 5
• There are 28 students in your math
class. Your teacher chooses 5
students at random to complete a
group project. Find the probabilityprobability
that you and your best friend are
chosen to work in the group.
Solution • The number of possible outcomes
• The number of favorable outcomes with
both of you in it.
• Probability = 2,600/98,280 = 5/189
PermutationPermutation
n is the total and r is the amount chosen
An arrangement or listing of objects where order IS important.
PermutationsORDER MATTERS!
Placement Examples: assigned seats, winning a race or running a race, 1st place, 2nd place, etc
PositionsExamples: President, Vice President, Secretary, Treasure
Specific job/choreExamples: Hand out markers, pass out papers, etc
PermutationPermutationss
Simplify each expression.
a. 12P2
b. 10P4
c. At a school science fair, ribbons are given for first, second, third, and fourth place, There are 20 exhibits in the fair. How many different arrangements of four winning exhibits are possible?
12 • 11 = 132
10 • 9 • 8 • 7 = 5,040
= 20P4 = 20 • 19 • 18 • 17 = 116,280
PermutationsExample 6• There are 50 runners in a race.
How many different ways can the
runners finish in 1st, 2nd, or 3rd?
Example 7
• Mike is picking 4 of his 12 friends
to go to the Braves game with
him. How many ways can he pick
the 4 friends that go with him?
Example 8
• A president and vice president
are being chosen from a group
of 20 people. How many ways
can this be done?
Example 9
• Mr. Shaw needs 3 people from
my class of 26 to come help
clean up the gym. How many
ways can I pick the 3 kids?
Example 10
How many ways can you
arrange 4 of the letters in the
word PANTHER?
Example 11
How many ways can you
arrange all of the letters in
the word FLOWER?