MAT 142 Lecture Video SeriesIntroduction to CombinatoricsObjectivesVocabularyA nickel, a dime and a quarter are tossed.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.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?FormulaSlide 10Find the value of:Creator and Producer Elizabeth Jones for The School of Mathematical and Statistical Sciences at Arizona State University Videographer Mike Jones ©2009 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State UniversityMAT 142Lecture Video SeriesIntroduction to CombinatoricsObjectives•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 •factorialA nickel, a dime and a quarter are tossed. Use the Fundamental Counting Principle to determine how many different outcomes are possible. Construct a tree diagram to list all possible outcomes.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?Formula123)3()2()1(! nnnnnn factorial0! = 1n is a positive integerCalculate each of the following 5!8!*6!!4!5!9Find the value of:!)!(!rrnnwhen n = 7 and r = 5.Creator and ProducerElizabeth Jones forThe School of Mathematical and Statistical SciencesatArizona State University VideographerMike Jones©2009 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State
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