how many license plates can be made using either three digits followed by three uppercase english letters or three lower case English letters followed by three digits?
Answers
Answer:
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Step-by-step explanation:
17,576,000 different
Example: How many different license plates can be made if each plate contains a sequence of three uppercase English letters followed by three digits? Solution: By the product rule, there are 26 ∙ 26 ∙ 26 ∙ 10 ∙ 10 ∙ 10 = 17,576,000 different possible license plates.
Answer:
The total number of ways the license plate can be prepared = 17576000 ways
Step-by-step explanation:
Given,
The license plate is made in the format
Three digits followed by three uppercase numbers
OR
Three lower case numbers followed by three digits
To find,
The number of possible license plates can be made in this manner
Solution:
The number of possible license plates that can be formed in both these cases is the same
The number of possible digits can be used = 10
The number of possible letters that can be used = 26
If we consider the first case, that is Three digits followed by three uppercase numbers
The first position from the left is a digit, which can be filled by 10ways
The second position from the left is a digit, which can be filled in 10 ways
The third position from the left is a digit, which can be filled in 10 ways
The fourth position from the left is a letter, which can be filled in 26 ways
The fifth position from the left is a letter, which can be filled in 26 ways
The sixth position from the left is a letter, which can be filled in 26 ways
Hence the total possibilities = 10×10×10×26×26×26
= 17576000
∴ The total number of ways the license plate can be prepared = 17576000 ways
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