Serial numbers for a product are to be made using 4 letters followed by 2 digits. The letters are to be taken from the first 6 letters of the alphabet, with no repeats. The digits are taken from the 10 digits 0, 1, 2, ..., 9, with no repeats. How many serial numbers can be generated?
Let's use constructive counting to find the answer. There are 6 choices for the first letter, then 5, and so on. For the numbers, there are 10 choices for the first number, and 9 for the second. Since these choices are independent of each other, we can multiply these numbers together. Does my explanation make sense?