Lecture 9: Principles of Counting

To apply some rule and product rule in solving problems.To apply the principles of counting in solving problems.Lecture 9: Principles of CountingActivity 9.1How many triangle can you draw using the 9 dots below as vertices?9.1 Sum RuleEveryday, there are 2 trains routine, 5 express bus routine, and 4 flight routine from Malaysia to Singapore. How many different ways can a passenger travel from Malaysia to Singapore?

9.1 Sum Rule9.1 Sum Rule9.1 Sum ruleExample:A student wants to borrow a book from library. He can choose the book from 3 business books, 5 computer science books, and 2 mathematics books. How many different ways he can borrow the book from library?

3 + 5 + 2 = 10 different ways to borrow a books.Product ruleIf John travel from town A to town C via town B. There are 3 routes from town A to town B and 2 routes from town B to town C. In how many ways can John travel from town A to town C?

Product RuleTaskProduct ruleProduct ruleEach of five cards contain digit 0, 1, 2, 3, 4 respectively. In how many ways these cards can be arranged to get an odd number?In how many ways these cards can be arranged to obtain a number that is greater than 30,000.In how many ways these cards can be arranged to obtain an odd number that is greater than 30,000? Product ruleExercise:In how many ways can the word Computing can be arranged?In how many ways can 3 persons be seated in an empty bus that has 44 seats. Permutation and CombinationAssume that A, B, C are 3 students. 2 students are selected to take a photo. In how many ways we can arrange the 2 students?

Is AB and BA be considered as the same photo?No.Is AB and BA considered as the same team?Yes.

When the order is important, the arrangement is called Permutation.When the order is not important, the selection is called Combination.ABACCBBACABCPermutationCombinationActivity 9.1How many triangle can you draw using the 9 dots below as vertices?CombinationExercise:A person buying a personal computer system is offered a choice of three models of the basic unit, two models of keyboard, and two models of printer. How many distinct systems can be purchased?Suppose that a code consists of five characters, two letters followed by three digits. Find the number of:codes; codes with distinct letter.Consider all positive integers with three digits. (Note that zero cannot be the first digit.) Find the number of them which are: greater than 700; odd;divisible by 5.