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Chapter 11: Problem 19

License plates in a particular state display two letters followed by three numbers, such as AT- 887 or BB-013. How many different license plates can be manufactured for this state?

Short Answer

Expert verified
The state can manufacture 676,000 different license plates.

Step by step solution

01

Calculating Letter Combinations

The English alphabet consists of 26 letters. The first part of the license plate contains 2 letters. This means that there are 26 options for the first letter and 26 options for the second letter. As per counting principle, the total combinations of letters that can be formed is \(26*26 = 676\). So we have 676 ways to choose the letters.
02

Calculating Number Combinations

The second part of the license plate consists of 3 numbers. As numbers range from 0 to 9, we have 10 possible options for each number. Therefore, there are \(10*10*10 = 1000\) combinations of numbers available.
03

Combining Letter and Number Combinations

Now the total number of license plates that can be manufactured is the multiplication of the combinations of the two parts. Which is \(676 * 1000 = 676000\).

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