Download presentation

Presentation is loading. Please wait.

1
Chapter 10 Counting Techniques

2
Combinations Section 10.3

3
**Combinations A selection of distinct objects**

without regard to order is a combination.

4
**Combination Formula The number of combinations of n**

objects, taken r at a time(order is not important and n r).

5
**Combination Formula The number of combinations of n**

objects, taken r at a time(order is not important n r).

6
**Combination Rule How many ways can 3 cards be chosen**

from a standard deck of 52 cards, disregarding the order of the selection? 52 x 51 x 50 3 x 2 x 1 52 nCr 3 = = 22,100

7
Combination Rule If 20 people all shake hands with each other, how many handshakes are there? 20 x 19 2 20 nCr 2 = = 190 The Greek alphabet has 24 letters. In how many ways can 3 different Greek letters be selected if the order does not matter? 24 x 23 x 22 3 x 2 x 1 24 nCr 3 = = 2024

8
**Combination Rule A committee is to consist of 3 members. If there**

are 4 men and 6 women available to serve on this committee, find the following: a. How many different committees can be formed? b. How many committees can be formed if each committee must consist of 2 men and 1 woman? 10 x 9 x 8 3 x 2 x 1 10 nCr 3 = = 120 4 nCr 2 x 6 nCr 1 = 6 x 6 = 36

9
**8 nCr 3 + 8 nCr 4 + 8 nCr 5 + 8 nCr 6 + 8 nCr 7 + 8 nCr 8 =**

Combination Rule How many different committees can be formed from 8 people if each committee must consist of at least 3 people? 8 nCr nCr nCr nCr nCr nCr 8 = = 219

10
**Combination Rule How many committees of 5 people can be**

formed from 9 men and 7 women if the committee must consist of less than 3 men? Determine what is acceptable for each gender in order to have a committee of five. Solution: 9 nCr 0 7 nCr nCr 1 7 nCr 4 +9 nCr 2 7 nCr 3 Acceptable Men Women 1 35 1 2 5 4 3 1596

11
**Combination Rule How many committees of 6 people can be**

formed from 9 men and 7 women if the committee must consist of more than 4 women? Determine what is acceptable for each gender in order to have a committee of six. Solution: Acceptable Men Women 9 nCr 1 7 nCr nCr 0 7 nCr 6 921 + 17 1 5 6 Notice 7 is not acceptable for the women. 196 END

Similar presentations

Presentation is loading. Please wait....

OK

9.5 Counting Subsets of a Set: Combinations

9.5 Counting Subsets of a Set: Combinations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on eia reporting Ppt on file system Ppt on social networking sites facebook Ppt on indian textile industries in ethiopia Ppt on gujarati culture Ppt on economic reforms in india 1991 economic reforms Ppt on universe and solar system Ppt on major types of industries Best ppt on online education Simple ppt on the circulatory system