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Counting Principle

Counting Principle. Section 8.6. Learning Goal. I will be able to solve counting problems using the Fundamental Counting Principle. . Example 1.

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Counting Principle

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  1. Counting Principle Section 8.6

  2. Learning Goal I will be able to solve counting problems using the Fundamental Counting Principle.

  3. Example 1 A box contains six balls, numbered one through six. A ball is drawn from the box, its number noted, and then it is placed back in the box. A second ball is drawn and its number noted. In how many different ways can a total of eight be obtained from the two balls? Consider ordered pairs of the form (1st draw, 2nd draw): (2,6), (3,5), (4,4), (5,3), (6,2) So there are five different ways to obtain a total of 8.

  4. Example 2 A box contains six balls numbered one through six. A ball is drawn from the box, its number noted, but it is NOT placed back in the box. A second ball is drawn and its number noted. In how many different ways can a total of eight be obtained from the two balls? Consider ordered pairs of the form (1st draw, 2nd draw): (2,6), (3,5),(5,3), (6,2) So there are four different ways to obtain a total of 8.

  5. Fundamental Counting Principle Let E1 and E2 be two events. The first event E1 can occur in m1 different ways. After E1 has occurred, E2 can occur in m2 different ways. The number of ways that the two events can occur is

  6. Example 3 How many different pairs of letters from the English alphabet are possible? There are 676 different pairs of letters possible.

  7. Example 4 Telephone numbers in the United States currently have 10 digits. The first three are the area code and the next seven are the local number. How many different telephone numbers are possible within each area code? (Note that at this time, a local telephone number cannot begin with 0 or 1.) There are 8,000,000 possible local telephone numbers within each area code.

  8. What did I learn today?

  9. Homework P. 609: 1 – 17 odds

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