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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.

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  • $\begingroup$ Hint: If you allow 10 digits in the first slot, you have only 9 remaining digits for the second slot... $\endgroup$ – David G. Stork Dec 4 '19 at 1:10
  • $\begingroup$ Makes sense, thank you! $\endgroup$ – Val Dec 4 '19 at 2:07
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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 = $(10 * 9 * 26 * 25 * 24)$

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  • $\begingroup$ Great, thank you for responding! $\endgroup$ – Val Dec 4 '19 at 2:07

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