Introduction to Combinatorics Objectives Use the Fundamental Counting

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. Construct a tree diagram to list all possible outcomes. Use the Fundamental Counting Principle to determine how many different outcomes are possible.

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 n factorial

Calculate each of the following 5! 8!*6!

Find the value of: when n = 7 and r = 5.

Counting Flow Chart