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Introduction to Combinatorics: Counting Methods and Applications

Learn how to apply the Fundamental Counting Principle, calculate factorials, and create tree diagrams to determine outcomes in combinatorics. Explore various scenarios like coin tossing and course selection to understand the concept better.

jerryphillips
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Introduction to Combinatorics: Counting Methods and Applications

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  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 ID’s 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

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