Question

Serial numbers for a product are to be made using 2 letters followed by 4 numbers. If the letters are to be taken from the first 5 letters of the alphabet with no repeats and the numbers are taken from the digits 0 through 9 with repeats possible, how many serial numbers can be generated?

Answer 1

First establish how many choices we have at each position:

1. "First five letters of the alphabet" --> 5 possibilities
2. "with no repeats" --> 4 possibilities (5 minus whatever was in spot 1) 
3. "digits 0 through 9" --> 10 possibilities 
4. "with repeats possible" --> 10 possibilities 
5. "with repeats possible" --> 10 possibilities 

Then we can calculate the total number of permutations by multiplying the the number of possibilities for each slot one after another:

$5 \times 4 \times 10 \times 10 \times 10 = 20,000$