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Introduction to Combinatorics

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.

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Introduction to Combinatorics

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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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