License plate numbers consist of two letters followed by a four-digit number, such as SB7893 or AY1042.

How many different plates are possible if letters can be repeated but digits cannot, and the four-digit number must be greater than 5500.


The answer to this question is 1,514,240.

I understand that "the letters that can be repeated" would be (26)^2 but I do not understand the second part.

How many four digit numbers are there that are greater than 5500?

9999 - 5500 + 1 = 4500

Now to count those that have all different digits.

So, if first number is 5 than second number must be 6,7,8 or 9 (because number must be greater than 5), which means 4 possibillities. Third number can be any number except 5 and the number in second place, which means 8 possibilities. And fourth number can be any of the last 7 possibilities.

So, how many numbers are there that are "good" for you, that begin with 5?
4*8*7 = 224

If a number starts with any of these numbers: 6,7,8,9 (4 possibilities), then second number can be any of the 9 numbers, third 8 numbers, last one 7 numbers.
4*9*8*7 = 2016

So, overall, how many "good" numbers are there? 2016 + 224 = 2240

How many license plates? 26*26*2240 = 1 514 240

Thanks! It makes sense now.