Lesson 9-5 Pages 387-390

Combinations

Lesson Check 9-4

What you will learn!

How to find the number of combinations of a set of

objects.

CombinationCombination

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?

RORO

RYRY

RGRG

RBRB

RIRI

RVRV

Let’s use ROYGBIV to represent the colors.

OROR

OYOY

OGOG

OBOB

OIOI

OVOV

YRYR

YOYO

YGYG

YBYB

YIYI

YVYV

GRGR

GOGO

GYGY

GBGB

GIGI

GVGV

BRBR

BOBO

BYBY

BGBG

BIBI

BVBV

IRIR

IOIO

IYIY

IGIG

IBIB

IVIV

VRVR

VOVO

VYVY

VGVG

VBVB

VIVI

Let’s eliminate all duplicates in the list.

RORO OROR YRYR GRGR BRBR IRIR VRVR

RYRY OYOY YOYO GOGO BOBO IOIO VOVO

RGRG OGOG YGYG GYGY BYBY IYIY VYVY

RBRB OBOB YBYB GBGB BGBG IGIG VGVG

RIRI OIOI YIYI GIGI BIBI IBIB VBVB

RVRV OVOV YVYV GVGV BVBV IVIV VIVI

RORO OROR YRYR GRGR BRBR IRIR VRVR

RYRY OYOY YOYO GOGO BOBO IOIO VOVO

RGRG OGOG YGYG GYGY BYBY IYIY VYVY

RBRB OBOB YBYB GBGB BGBG IGIG VGVG

RIRI OIOI YIYI GIGI BIBI IBIB VBVB

RVRV OVOV YVYV GVGV BVBV IVIV VIVI

There are 21 different pairs of colors.

RORO

RYRY OYOY

RGRG OGOG YGYG

RBRB OBOB YBYB GBGB

RIRI OIOI YIYI GIGI BIBI

RVRV OVOV YVYV GVGV BVBV IVIV

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.

212

42

!2

67

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.

ways566

336

!3

678

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.

ways336678

Page 389

Guided Practice

#’s 4-6

Pages 387-388 with someone at home and study

examples!

Read:

Homework: Page 389-390

#’s 7-16 all

#’s 19-32

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.

452

90

!2

910

45 exchanges!