Lesson 12-7 Pages 641-645

Permutations and Combinations

What you will learn!1. How to use permutations.

2. How to use combinations.

PermutationPermutationFactorialFactorialCombinationCombination

What you really need to know!

PermutatioPermutationn

An arrangement or listing in An arrangement or listing in which order is importantwhich order is important

P(m,n) means m number of P(m,n) means m number of choices taken n at a timechoices taken n at a time

P(5,2) = 5 x 4 = 20P(5,2) = 5 x 4 = 20

CombinatiCombinationon

An arrangement or listing in An arrangement or listing in which order is not importantwhich order is not important

C(m,n) = P(m,n) C(m,n) = P(m,n) ÷ n!÷ n!

C(6,2) = 6 x 5 C(6,2) = 6 x 5 ÷ (2x1) = 15÷ (2x1) = 15

The Reyes family will visit a complex of theme parks during their summer vacation. They have a four-day pass good at one park per day; they can choose from seven parks. How many different ways can they arrange their vacation schedule?

The order in which they visit the parks is important.

)4,7(P

7 choices for the 1st day6 choices for the 2nd day5 choices for the 3rd day4 choices for the 4th day

This arrangement is a permutation.

4567 840

How many five-digit numbers can be made from the digits 2, 4, 5, 8, and 9 if each digit is used only once?

The order in which the numbers are picked is important.

)5,5(P

5 choices for the 1st digit4 choices remaining for the 2nd digit3 choices remaining for the 3rd digit2 choices remaining for the 4th digit1 choice remaining for the 5th digit

This arrangement is a permutation.

12345 120

Find the value of 12!123456789101112

479,001,600

How many ways can a window dresser choose two hats out of a fedora, a bowler, and a sombrero?

Since order is not important, this arrangement is a combination.

FBFBFSFSBFBFBSBSSFSFSBSB

Cross off any arrangements that are the same as another one.

3 ways!

How many ways can a window dresser choose two hats out of a fedora, a bowler, and a sombrero?

)2,3(C!2

23 3

2

6

How many ways can a customer choose two pens from a purple, orange, green, red, or black pen?

)2,5(C!2

45 10

2

20

Geometry: Find the number of line segments that can be drawn between any two vertices of a hexagon.

This is a combination.

6 vertices taken 2 at a time.

)2,6(C!2

56 15

2

30

Page 643

Guided Practice

#’s 4-9

Pages 641-643 with someone at home and

study examples!

Read:

Homework: Pages 644-645

#’s 10-28 all

#’s 32-44

Lesson Check 12-7

Page

754

Lesson 12-7

What is the probability of winning a multi-state lottery game where the winning number is made up of 6 numbers from 1 to 50 chosen at random? All numbers are eligible each draw.

There are 50 choices for the first number, 50 choices for the second number, 50 choices for the third number, and so on.

50 50 50 50 50 50 = 15,625,000,000

There is only 1 winning number.

000,000,625,15

1

There are 50 choices for the first number, 50 choices for the second number, 50 choices for the third number, and so on.

50 50 50 50 50 50 = 15,625,000,000 ÷ 6!

There is only 1 winning number.

389,701,21

1

PA Cash 5:There are 39 choices for the first number, 38 choices for the second number, 37 choices for the third number, and so on.39 38 37 36 35 = 69,090,840 ÷ 5!

There is only 1 winning number.

757,575

1

Power-Ball: 55 for first 5, 42 for Power-ballThere are 55 choices for the first number, 54 choices for the second number, 53 choices for the third number, and so on.55 54 53 52 51 = 417451320 ÷ 5! x 42

There is only 1 winning number.

962,107,146

1