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 17576 Thus, the number of license plates is 175760000 ways to perform steps 1-3, and there are 10000 ways to perform the remaining steps (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 1 final step is 1 and the number of ways to place the 0 in th . Thus, the answer is 676000 (c) How many license plates could begin with BWC? In this case, the number of ways to perform steps 1-3 is 1 Thus, the answer is 10000 (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? Enter an exact number.
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 17576 Thus, the number of license plates is 175760000 ways to perform steps 1-3, and there are 10000 ways to perform the remaining steps (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 1 final step is 1 and the number of ways to place the 0 in th . Thus, the answer is 676000 (c) How many license plates could begin with BWC? In this case, the number of ways to perform steps 1-3 is 1 Thus, the answer is 10000 (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? Enter an exact number.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
17576
Thus, the number of license plates is 175760000
ways to perform steps 1-3, and there are 10000
ways to perform the remaining steps.
(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 1
final step is 1
and the number of ways to place the 0 in the
. Thus, the answer is 676000
(c) How many license plates could begin with BWC?
In this case, the number of ways to perform steps 1-3 is 1
Thus, the answer is 10000
(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?
Enter an exact number.
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