Serial numbers for a product are to be using 3 letters followed by 4 digits. The letters are to be t | MathCelebrity Forum

# Serial numbers for a product are to be using 3 letters followed by 4 digits. The letters are to be t

#### math_celebrity

Staff member
Serial numbers for a product are to be using 3 letters followed by 4 digits. The letters are to be taken from the first 8 letters of the alphabet with no repeats. The digits are taken from numbers 0-9 with no repeats. How many serial numbers can be generated

The serial number is organized with letters (L) and digits (D) like this:
LLLDDDD

Here's how we get the serial number:
1. The first letter can be any of 8 letters A-H
2. The second letter can be any 7 of 8 letters A-H
3. The third letter can be any 6 of 8 letters A-H
4. The fourth digit can be any of 10 digits 0-9
5. The fifth digit can be any 9 of 10 digits 0-9
6. The sixth digit can be any 8 of 10 digits 0-9
7. The seventh digit can be any 7 of 10 digits 0-9
We multiply all possibilities:
8 * 7 * 6 * 10 * 9 * 8 * 7
1,693,440