If repetition is not allowed, how many different license plates are possible if two letters are followed by four digits?

Answer 1

These problems often introduce some extra info we don't necessarily need. In this case, the fact that this is going on license plates doesn't impact our calculation, so let's set that aside. The important parts are:

No repetition

2 Letters

4 Digits

Let's break this down and see how we would select each item, one-by-one:

1. (26) This means we have 26 options for the first item (since there are 26 letters in the alphabet)
2. (25) Then we have 25 options for the second item (since we can't use that letter we picked to go first)
3. (10) Next, we're at 10 options for digits (0 through 9)
4. ( 9 ) Since we can't repeat whatever digit came before, we're down to 9 options for this item.
5. ( 8 ) Lastly, we can't repeat either of the previous digits, leaving us with 8 options.

If you remember back to your tree diagrams, each time it branches off, it sort of multiplies the number of total branches at the end. This happens any time we make a combination of decisions - the outcomes multiply. So, if we multiply 26*25*10*9*8, we'll get our answer.

Answer 2

(26)(25)(10)(9)(8)(7) = ?