Basic Probability Calculations

1
Basic Probability Calculations

• Cafeteria Method
• Multiplication rule
• General Assignment Method
• Combinations
• Specific Assignment Method
• Permutations
• Partitioning Method
• Permutations

2
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?
• 532 30 orders
• There are 30 different ways to make an order.

3
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?

4
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

5
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, n1 3 n2 2 n3 2),
• 210 permutations
• Note that there are three partitions and the
  total number of partitions (beds) available
  (n1n2n3) the total number of students to be
  assigned (n).