Serial numbers for a product are to be made using 3 letters followed by 4 digits. The letters are to be taken from the first letters of the alphabet, with no repeats. The digits are taken from the 10 digits, with no repeats. How many serial numbers can be generated?

30,240 ways, if I am restricted to using A, B, and C for letters

Step-by-step explanation:

This uses Combinatorics from Discrete Math.

so.

3 letters and 4 digits.

26 letters from alphabet, but you want to choose first letters. no repeats ...

Does this mean only letters A, B, and C?

digits from 10 digits ...

I imagine 7 empty slots, and the number of ways they occur together is by the product of the number of choices each box has.

3*2*1 * 10*9*8*7 = 6 * 5040 = 30,240 ways