Download presentation

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

Chapter 1. Combinatorial Analysis – Introduction

Chapter 1. Combinatorial Analysis – Introduction

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google