MAT 142 Lecture Video Series. Introduction to Combinatorics.
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Transcript of MAT 142 Lecture Video Series. Introduction to Combinatorics.
![Page 1: MAT 142 Lecture Video Series. Introduction to Combinatorics.](https://reader035.fdocuments.net/reader035/viewer/2022062408/56649f0d5503460f94c21910/html5/thumbnails/1.jpg)
MAT 142Lecture Video
Series
![Page 2: MAT 142 Lecture Video Series. Introduction to Combinatorics.](https://reader035.fdocuments.net/reader035/viewer/2022062408/56649f0d5503460f94c21910/html5/thumbnails/2.jpg)
Introduction to Combinatorics
![Page 3: MAT 142 Lecture Video Series. Introduction to Combinatorics.](https://reader035.fdocuments.net/reader035/viewer/2022062408/56649f0d5503460f94c21910/html5/thumbnails/3.jpg)
Objectives
• Use the Fundamental Counting Principle to determine a number of outcomes.
• Calculate a factorial. • Make a tree diagram to list all
outcomes.
![Page 4: MAT 142 Lecture Video Series. Introduction to Combinatorics.](https://reader035.fdocuments.net/reader035/viewer/2022062408/56649f0d5503460f94c21910/html5/thumbnails/4.jpg)
Vocabulary
• tree diagram • Fundamental Counting Principle • factorial
![Page 5: MAT 142 Lecture Video Series. Introduction to Combinatorics.](https://reader035.fdocuments.net/reader035/viewer/2022062408/56649f0d5503460f94c21910/html5/thumbnails/5.jpg)
A nickel, a dime and a quarter are tossed.
Use the Fundamental Counting Principle to determine how many different outcomes are possible.
Construct a tree diagram to list all possible outcomes.
![Page 6: MAT 142 Lecture Video Series. Introduction to Combinatorics.](https://reader035.fdocuments.net/reader035/viewer/2022062408/56649f0d5503460f94c21910/html5/thumbnails/6.jpg)
To fulfill certain requirements for a degree, a student must take one course each from the following groups: health, civics, critical thinking, and elective. If there are four health, three civics, six critical thinking, and ten elective courses, how many different options for fulfilling the requirements does a student have?
![Page 7: MAT 142 Lecture Video Series. Introduction to Combinatorics.](https://reader035.fdocuments.net/reader035/viewer/2022062408/56649f0d5503460f94c21910/html5/thumbnails/7.jpg)
How many different Zip Codes are possible using.
• the old style (five digits)
• the new style (nine digits)
![Page 8: MAT 142 Lecture Video Series. Introduction to Combinatorics.](https://reader035.fdocuments.net/reader035/viewer/2022062408/56649f0d5503460f94c21910/html5/thumbnails/8.jpg)
Each student at State University has a student ID number consisting of four digits (the first digit is nonzero and digits may be repeated) followed by three of the letters A, B, C, D, and E (letters may not be repeated). How many different student ID’s are possible?
![Page 9: MAT 142 Lecture Video Series. Introduction to Combinatorics.](https://reader035.fdocuments.net/reader035/viewer/2022062408/56649f0d5503460f94c21910/html5/thumbnails/9.jpg)
Formula
123)3()2()1(! nnnnn
n factorial
0! = 1
n is a positive integer
![Page 10: MAT 142 Lecture Video Series. Introduction to Combinatorics.](https://reader035.fdocuments.net/reader035/viewer/2022062408/56649f0d5503460f94c21910/html5/thumbnails/10.jpg)
Calculate each of the following
5!
8!*6!
!4!5!9
![Page 11: MAT 142 Lecture Video Series. Introduction to Combinatorics.](https://reader035.fdocuments.net/reader035/viewer/2022062408/56649f0d5503460f94c21910/html5/thumbnails/11.jpg)
Find the value of:
!)!(!rrn
n
when n = 7 and r = 5.
![Page 12: MAT 142 Lecture Video Series. Introduction to Combinatorics.](https://reader035.fdocuments.net/reader035/viewer/2022062408/56649f0d5503460f94c21910/html5/thumbnails/12.jpg)
Creator and Producer
Elizabeth Jones
for
The School of Mathematical and Statistical Sciences
atArizona State University
Videographer
Mike Jones
©2009 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State University