Lesson 12-7 Pages 641-645 Permutations and Combinations.

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Presentation transcript:

Lesson 12-7 Pages Permutations and Combinations

What you will learn! 1. How to use permutations. 2. How to use combinations.

PermutationFactorial Combination

What you really need to know!Permutation An arrangement or listing in which order is important P(m,n) means m number of choices taken n at a time P(5,2) = 5 x 4 = 20 Combination An arrangement or listing in which order is not important C(m,n) = P(m,n) ÷ n! C(6,2) = 6 x 5 ÷ (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. 7 choices for the 1st day 6 choices for the 2nd day 5 choices for the 3rd day 4 choices for the 4th day This arrangement is a permutation.

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 choices for the 1 st digit 4 choices remaining for the 2 nd digit 3 choices remaining for the 3 rd digit 2 choices remaining for the 4 th digit 1 choice remaining for the 5 th digit This arrangement is a permutation.

Find the value of 12! 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.FB FS BF BS SF SB 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?

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

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.

Page 643 Guided Practice #’s 4-9

Pages with someone at home and study examples! Read:

Homework: Pages #’s all #’s 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.

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.

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.

Power-Ball: 55 for first 5, 42 for Power-ball There 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 = ÷ 5! x 42 There is only 1 winning number.