ESSENTIAL STATISTICS 2 E William Navidi and Barry

ESSENTIAL STATISTICS 2 E William Navidi and Barry Monk ©Mc. Graw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of Mc. Graw-Hill Education.

Counting Section 4. 4 ©Mc. Graw-Hill Education.

Objectives 1. Count the number of ways a sequence of operations can be performed 2. Count the number of permutations 3. Count the number of combinations ©Mc. Graw-Hill Education.

Objective 1 Count the number of ways a sequence of operations can be performed ©Mc. Graw-Hill Education.

The Fundamental Principle of Counting • Example: A certain make of automobile is available in any of three colors: red, blue, or green, and comes with either a large or small engine. In how many ways can a buyer choose a car? There are 3 choices of color and 2 choices of engine. The total number of choices is 3· 2 = 6. ©Mc. Graw-Hill Education.

Example: Fundamental Principle of Counting License plates in a certain state contain three letters followed by three digits. How many different license plates can be made? Solution: There are six operations in all; choosing three letters and choosing three digits. There are 26 ways to choose each letter and 10 ways to choose each digit. The total number of license plates is therefore 26· 26· 10· 10 = 17, 576, 000. ©Mc. Graw-Hill Education.

Objective 2 Count the number of permutations ©Mc. Graw-Hill Education.

Permutations • ©Mc. Graw-Hill Education.

Example: Permutations Five runners run a race. One of them will finish first, another will finish second, and so on. In how many different orders can they finish? The number of different orders the runners can finish is 5! = 5· 4· 3· 2· 1 = 120. Ten runners run a race. The first-place finisher will win a gold medal, the second-place finisher will win a silver medal, and the third-place finisher will win a bronze medal. In how many different ways can the medals be awarded? We use the Fundamental Principle of Counting. There are 10 possible choices for the gold medal winner. Once the gold medal winner is determined, there are nine remaining choices for the silver medal. Finally, there are eight choices for the bronze medal. The total number of ways the medals can be awarded is 10· 9· 8 = 720. ©Mc. Graw-Hill Education.

• ©Mc. Graw-Hill Education.

Example: Combination • ©Mc. Graw-Hill Education.

Permutations and Combinations on the TI-84 Calculator commands for permutations and combinations are accessed by pressing MATH and scrolling to the PRB menu. • ©Mc. Graw-Hill Education.