The plate has 2 digits followed by 3 letters. How many different plates are there without a repeated symbol? I know how to get every single possibility (10 * 10 * 26 * 26 * 26), but that includes repeated symbols.
Without repeated number for the first number, you would have 10 options, now having 1 number, for the second number there are only 9 options left since you can't repeat the first one. The same goes for the alphabet first letter has 26 options, second one 25, the third one 24.
Hence every possibility = $(10 * 9 * 26 * 25 * 24)$