Suppose that in a certain state, all automobile license plates have three uppercase letters followed by four digits. Use the method illustrated in Examplė 9.2.2 tổ answer Lhe ToiIUWINg (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 and the number of ways to place the 0 in the final step is Thus, the answer is (c) How many license plates could begin with XIL? In this case, the number of ways to perform steps 1-3 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?
Suppose that in a certain state, all automobile license plates have three uppercase letters followed by four digits. Use the method illustrated in Examplė 9.2.2 tổ answer Lhe ToiIUWINg (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 and the number of ways to place the 0 in the final step is Thus, the answer is (c) How many license plates could begin with XIL? In this case, the number of ways to perform steps 1-3 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?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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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
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
and the number of ways to place the 0 in the final step is
Thus, the answer is
(c) How many license plates could begin with XIL?
In this case, the number of ways to perform steps 1-3 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?
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