Introduction to Combinatorics Page 1 of 2 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 =!n Possible Classroom Examples: A nickel, a dime and a quarter are tossed. a. Construct a tree diagram to list all possible outcomes. b. 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. a. the old style (five digits) b. the new style (nine digits)Introduction to Combinatorics Page 2 of 2 Each student and 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? Calculate each of the following • !5 • !6!8∗ • !4!5!9∗ Find the value of !)!*(!rrnn− when 7=n and
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