# Given 2 digits and 3 letters, how many different license plates are possible without a repeated symbol?

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.

• Hint: If you allow 10 digits in the first slot, you have only 9 remaining digits for the second slot... – David G. Stork Dec 4 '19 at 1:10
• Makes sense, thank you! – Val Dec 4 '19 at 2:07

Hence every possibility = $$(10 * 9 * 26 * 25 * 24)$$