Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![**Question 10**
In Virginia, each automobile license plate consists of a single digit followed by three letters, followed by three digits. How many distinct license plates can be formed if there are no restrictions on the digits or letters?
A) 175,760
B) 175,756,000
C) 10,757,600
D) 17,575,600
E) 17,576
**Options:**
- O A
- O B
- O C
- O D
- O E
**Instructions:**
Click Save and Submit to save and submit. Click Save All Answers to save all answers.
**Explanation:**
To solve the problem, consider the structure of the license plate:
1. **Single digit:** There are 10 possibilities (0-9).
2. **Three letters:** Each letter has 26 possibilities (A-Z). Therefore, for three letters you have \(26 \times 26 \times 26\) possibilities.
3. **Three digits:** Each digit has 10 possibilities. Therefore, for three digits you have \(10 \times 10 \times 10\) possibilities.
The total number of license plates can be calculated by multiplying these possibilities:
\[10 \times (26^3) \times (10^3) = 17,576,000\]
Therefore, the correct answer is **Option D) 17,576,000**.](https://content.bartleby.com/qna-images/question/e275248a-cf4e-467d-a30e-f2de7097d675/a6519b67-0453-46f0-b4d7-c7804a6e40ff/6vq7fd8_processed.jpeg)
Transcribed Image Text:**Question 10**
In Virginia, each automobile license plate consists of a single digit followed by three letters, followed by three digits. How many distinct license plates can be formed if there are no restrictions on the digits or letters?
A) 175,760
B) 175,756,000
C) 10,757,600
D) 17,575,600
E) 17,576
**Options:**
- O A
- O B
- O C
- O D
- O E
**Instructions:**
Click Save and Submit to save and submit. Click Save All Answers to save all answers.
**Explanation:**
To solve the problem, consider the structure of the license plate:
1. **Single digit:** There are 10 possibilities (0-9).
2. **Three letters:** Each letter has 26 possibilities (A-Z). Therefore, for three letters you have \(26 \times 26 \times 26\) possibilities.
3. **Three digits:** Each digit has 10 possibilities. Therefore, for three digits you have \(10 \times 10 \times 10\) possibilities.
The total number of license plates can be calculated by multiplying these possibilities:
\[10 \times (26^3) \times (10^3) = 17,576,000\]
Therefore, the correct answer is **Option D) 17,576,000**.
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