Acc Math 1 EQ: What is the difference between a permutation and combination?

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?