Introduction to Combinatorics

1
Introduction to Combinatorics
2
Objectives

• Use the Fundamental Counting Principle to
  determine a number of outcomes.
• Calculate a factorial.
• Make a tree diagram to list all outcomes.

3
Vocabulary

• tree diagram
• Fundamental Counting Principle
• factorial

4
A nickel, a dime and a quarter are tossed.
Construct a tree diagram to list all possible
outcomes.
Use the Fundamental Counting Principle to
determine how many different outcomes are
possible.
5
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?
6
How many different Zip Codes are possible using.

• the old style (five digits)
• the new style (nine digits) 

7
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 IDs are possible?
8
Formula
n factorial
9
Calculate each of the following
5!
8!6!
10
Find the value of
when n 7 and r 5.
11
Counting Flow Chart