Question

The standard configuration for an Idaho license plate is 3 letter]followed by 5 digits.

How many different license plates are possible if letters and digits can not be repeated?

Answer 1

Answer: 471,744,000

Delete the commas if needed. This is one single number between 471 million and 472 million

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Step-by-step explanation:

We have 26 letters for the first slot, then 25 for the second, and 24 for the third. We count down like this because we cannot reuse letters.

There are 26*25*24 = 15,600 ways to pick the three letters where repeats aren't allowed.

As for the numbers, we have 10 single digits (0 through 9) for the first numeric slot, then 9 for the next, and so on until we reach 6

So we have 10*9*8*7*6 = 30,240 ways to select the five numbers.

In all, there are (15,600)*(30,240) = 471,744,000 different license plates possible. This number is between 471 million and 472 million.