Basic Probability Calculations Cafeteria Method Multiplication rule General

Basic Probability Calculations § Cafeteria Method § Multiplication rule § General Assignment Method § Combinations § Specific Assignment Method § Permutations § Partitioning Method § Permutations JMB Chapter 2 c Review EGR 252. 001 Spring 2009 1

Cafeteria Problems § Pick one from each menu to define a single combination § Assuming you must pick one from each category, you apply the multiplication rule § Example: How many orders are possible if you select from 5 entrees, 3 desserts, and 2 drinks? 5*3*2 = 30 orders § There are 30 different ways to make an order. § JMB Chapter 2 c Review EGR 252. 001 Spring 2009 2

General Assignment Problems § Selections of subsets without regard to order § Example: How many ways can we select 3 different books from a set of 12 different books? § Example: How many ways can we assign 5 different teachers to participate in a summer training program if there are 2 openings? JMB Chapter 2 c Review EGR 252. 001 Spring 2009 3

Specific Assignment Problems § How many ways can we assign 3 students to position of president, vice president or secretary if there are six people in the club? § (n = 6, r = 3), permutations § Example: Five different teachers are available to teach EGR 252 and EGR 312 this term. In how many ways can we staff the courses if each teacher is only allowed to teach one course? § (n = 5, r = 2), permutations JMB Chapter 2 c Review EGR 252. 001 Spring 2009 4

Partitioning Problems § Example 2. 20 § In how many ways can we assign 7 students to one triple and two double rooms during a conference? § (n = 7, n 1 = 3 n 2 = 2 n 3 = 2), § 210 permutations § Note that there are three partitions and the total number of partitions (beds) available (n 1+n 2+n 3) = the total number of students to be assigned (n). JMB Chapter 2 c Review EGR 252. 001 Spring 2009 5