Question

The serial number on a dollar bill consists of a letter, followed by eight digits and then a letter. How many different serial numbers are possible if letters and digits cannot be repeated?

Answer 1

Answer 2

To calculate the number of different possible serial numbers, we need to consider the number of choices for each position in the serial number.

1. For the first letter: There are 26 choices (A to Z).

2. For the eight digits: There are 10 choices for each digit (0 to 9), and since digits cannot be repeated, we have 10 choices for the first digit, 9 choices for the second digit, 8 choices for the third digit, and so on, until 3 choices for the eighth digit.

3. For the last letter: There are 26 choices (A to Z).

To find the total number of possible serial numbers, we need to multiply the number of choices for each position:

Total number of possible serial numbers = 26 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 26

Now, let's calculate this value:

Total number of possible serial numbers = 26 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 26 Total number of possible serial numbers = 62,208,000

There are 62,208,000 different possible serial numbers if letters and digits cannot be repeated.