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Suppose that in a certain state, all automobile license plates have three uppercase letters followed by four digits. Use the method illustrated in Example 9.2.2 to answer the following questions. (a) How many different license plates are possible? To answer this question, think of creating a license plate as a 6-step process, where steps 1-3 are to choose the uppercase letters to put in positions 1-3 and the remaining steps are to choose the digits put in the remaining positions. There are ways to perform steps 1-3, and there are ways to perform the remaining steps. Thus, the number of license plates is (b) How many license plates could begin with and end in 0? In this case, the number of ways to place the A in Step 1 is (c) How many license plates could begin with HMB? In this case, the number of ways to perform steps 1-3 is and the number of ways to place the 0 in the final step is . Thus, the answer is (d) How many license plates are possible in which all the letters and digits are distinct? (e) How many license plates could begin with AB and have all letters and digits distinct? Thus, the answer is

Suppose that in a certain state, all automobile license plates have three uppercase letters followed by four digits. Use the method illustrated in Example 9.2.2 to answer the following questions. (a) How many different license plates are possible? To answer this question, think of creating a license plate as a 6-step process, where steps 1-3 are to choose the uppercase letters to put in positions 1-3 and the remaining steps are to choose the digits put in the remaining positions. There are ways to perform steps 1-3, and there are ways to perform the remaining steps. Thus, the number of license plates is (b) How many license plates could begin with and end in 0? In this case, the number of ways to place the A in Step 1 is (c) How many license plates could begin with HMB? In this case, the number of ways to perform steps 1-3 is and the number of ways to place the 0 in the final step is . Thus, the answer is (d) How many license plates are possible in which all the letters and digits are distinct? (e) How many license plates could begin with AB and have all letters and digits distinct? Thus, the answer is

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.CT: Chapter Test
Problem 1CT: Alice and Bill have four grandchildren, and they have three framed pictures of each grandchild. They...
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Suppose that in a certain state, all automobile license plates have three uppercase letters followed by four digits. Use the method illustrated in Example 9.2.2 to answer the following questions. (a) How many different license plates are possible? To answer this question, think of creating a license plate as a 6-step process, where steps 1-3 are to choose the uppercase letters to put in positions 1-3 and the remaining steps are to choose the digits to put in the remaining positions. There are ways to perform steps 1-3, and there are ways to perform the remaining steps. Thus, the number of license plates is (b) How many license plates could begin with A and end in 0? In this case, the number of ways to place the A in Step 1 is (c) How many license plates could begin with HMB? In this case, the number of ways to perform steps 1-3 is and the number of ways to place the 0 in the final step is Thus, the answer is (d) How many license plates are possible in which all the letters and digits are distinct? (e) How many license plates could begin with AB and have all letters and digits distinct? Thus, the answer is
Transcribed Image Text:Suppose that in a certain state, all automobile license plates have three uppercase letters followed by four digits. Use the method illustrated in Example 9.2.2 to answer the following questions. (a) How many different license plates are possible? To answer this question, think of creating a license plate as a 6-step process, where steps 1-3 are to choose the uppercase letters to put in positions 1-3 and the remaining steps are to choose the digits to put in the remaining positions. There are ways to perform steps 1-3, and there are ways to perform the remaining steps. Thus, the number of license plates is (b) How many license plates could begin with A and end in 0? In this case, the number of ways to place the A in Step 1 is (c) How many license plates could begin with HMB? In this case, the number of ways to perform steps 1-3 is and the number of ways to place the 0 in the final step is Thus, the answer is (d) How many license plates are possible in which all the letters and digits are distinct? (e) How many license plates could begin with AB and have all letters and digits distinct? Thus, the answer is
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