Lesson 9-5 Pages 387-390 Combinations Lesson Check 9-4.

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Presentation transcript:

Lesson 9-5 Pages Combinations Lesson Check 9-4

What you will learn! How to find the number of combinations of a set of objects.

Combination

What you really need to know! An arrangement, or listing, of objects in which order is not important is called a combination.

What you really need to know! You can find the number of combinations of objects by dividing the number of permutations of the entire set by the number of ways each smaller set can be arranged.

Link to Pre-Made Lesson

Example 1: Ada can select from seven paint colors for her room. She wants to choose two colors. How many different pairs of colors can she choose?

RO RY RG RB RI RV Let’s use ROYGBIV to represent the colors.OROY OG OB OI OVYRYO YG YB YI YVGRGO GY GB GI GVBRBO BY BG BI BVIRIO IY IG IB IVVRVO VY VG VB VI

Let’s eliminate all duplicates in the list.ROORYRGRBRIRVR RYOYYOGOBOIOVO RGOGYGGYBYIYVY RBOBYBGBBGIGVG RIOIYIGIBIIBVB RVOVYVGVBVIVVIROORYRGRBRIRVRRYOYYOGOBOIOVO RGOGYGGYBYIYVY RBOBYBGBBGIGVG RIOIYIGIBIIBVB RVOVYVGVBVIVVI

There are 21 different pairs of colors.RO RYOY RGOGYG RBOBYBGB RIOIYIGIBI RVOVYVGVBVIV

Example 1: Method 2 There are 7 choices for the first color and 6 choices for the second color. There are 2 ways to arrange two colors. 21 pairs of colors!

Example 2: Tell whether the situation represents a permutation or combination. Then solve the problem. From an eight-member track team, three members will be selected to represent the team at the state meet. How many ways can these three members be selected. Combination!

There are 8 members for the first position, 7 for the second and 6 for the third. 3 people can be arranged in 6 ways.

Example 3: Tell whether the situation represents a permutation or combination. Then solve the problem. In how many ways can you choose the first, second, and third runners in a relay race from the eight members of the track team? Permutation!

There are 8 members for the first position, 7 for the second and 6 for the third.

Page 389 Guided Practice #’s 4-6

Pages with someone at home and study examples! Read:

Homework: Page #’s 7-16 all #’s Lesson Check 9-5

Link to Lesson 9-5 Review Problems

Page 586 Lesson 9-5

Lesson Check 9-5

Example 2: Ten managers attend a business meeting. Each person exchanges names with each other person once. How many introductions will there be?

Example 2: There are 10 choices for one of the people exchanging names and 9 choices for the second person. There are 2 ways to arrange two people. 45 exchanges!