![]() ![]() In how many different ways can this man wear a suit, a shirt and a pair of shoes? Problem 5 A man has 3 different suits, 4 different shirts and 5 different pairs of shoes. The total number N of different ways that someone can go from city A to city C, passing by city B is.In how many ways can someone go from city A to city C passing by city B? Problem 4 There are 3 different roads from city A to city B and 2 different roads from city B to city C. The total number N of different ways that the students can select his 3 books is given by.In how many different ways can a student select a book of mathematics, a book of chemistry and a book of science? N = 1 × 1 × 9 × 10 × 10 × 10 × 10 × 10 × 10 = 9,000,000Ī student can select one of 6 different mathematics books, one of 3 different chemistry books and one of 4 different science books. Using the counting principle, the total number of possible telephone numbers is given by.The 2nd, 3rd, 4th, 5th, 6th and 7 th digits of the local code can be any digit, hence 10 choices each. The first digit of the local code can be any digit except 0, so 9 choices. The second digit of the area code is 1, no choice or one choice only. The first digit of the area code is 0, no choice which is in fact one choice only. The diagram below shows the number of choices for each digit. ![]() How many different telephone numbers are possible within a given area code in this country? ![]() The last 7 digits are the local number and cannot begin with 0. The first two digits are the area code (03) and are the same within a given area. Problem 2 In a certain country telephone numbers have 9 digits. Using the counting principle used in the introduction above, the number of all possible computer systems that can be bought is given by.The diagram below shows each item with the number of choices the customer has. A customer can choose one monitor, one keyboard, one computer and one printer. ![]() Determine the number of possible systems that a customer can choose from. To buy a computer system, a customer can choose one of 4 monitors, one of 2 keyboards, one of 4 computers and one of 3 printers. different ways respectively, the number of ways that all events can occur is equal to Using the above problem, we can generalize and write a formula related to counting as follows: It is clear from the tree diagram above that the total number N of choices may be calculated as follows: Let n3 be the number of choices of the mathematics course, here n3 = 2. Let n2 be the number of choices of the science course, here n2 = 2. Let n1 be the number of choices of the physics course, here n1 = 3. The total number of choices may be calculated as follows: The different ways in which the 3 courses may be selected are: Then the second column shows the 2 possible choices of the science course and the last column shows the 2 possible choices for the mathematics course. The first column on the left shows the 3 possible choices of the physics course: P1, P2 or P3. Let us use a tree diagram that shows all possible choices. In how many ways can this student select the 3 courses he has to take? He may choose one of 3 physics courses (P1, P2, P3), one of 2 science courses (S1, S2) and one of 2 mathematics courses (M1, M2). Let us start by introducing the counting principle using an example.Ī student has to take one course of physics, one of science and one of mathematics. Counting problems are presented along with their detailed solutions and detailed explanations. ![]()
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