MAT 142Lecture Video

Series

Introduction to Combinatorics

Objectives

• Use the Fundamental Counting Principle to determine a number of outcomes.

• Calculate a factorial. • Make a tree diagram to list all

outcomes.

Vocabulary

• tree diagram • Fundamental Counting Principle • factorial

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.

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?

How many different Zip Codes are possible using.

• the old style (five digits)

• the new style (nine digits) 

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?

Formula

123)3()2()1(! nnnnn

n factorial

0! = 1

n is a positive integer

Calculate each of the following

5!

8!*6!

!4!5!9

Find the value of:

!)!(!rrn

n

when n = 7 and r = 5.

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