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How many combinations that are 5 characters can be made with numbers 0-9 and letters A-Z and all caps (e.g. ASX51)?

Ahmed Eddine
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    Do you allow repetition ? Do you take the order into account ? – TheSilverDoe Nov 05 '20 at 13:51
  • Im not really sure what you mean but @marya answered – Ahmed Eddine Nov 10 '20 at 16:07
  • I meant that "combination" is not so clear : is $AAAAA$ a valid combination, or must the characters be all different ? Also, is $ASX51$ the same combination as $SAX51$ (because it has the same characters), or is it a different one ? – TheSilverDoe Nov 10 '20 at 16:09

1 Answers1

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There are $26$ characters in the alphabet, and there are $10$ in $0$-$9$. So we have $36$ characters overall.

Therefore, there are $$ \binom{36}{5}=\frac{36!}{(36-5)!5!}=\frac{36!}{31!5!}=\frac{36\cdot 35\cdot 34\cdot 33\cdot 32}{5\cdot4\cdot3\cdot2}=3\cdot7\cdot 17\cdot 33\cdot 32=376,992 $$ different $5$ characters.

marya
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  • @AhmedEddine If the order of the characters is important, the answer changes to $$5! \times \binom{36}{5}.$$ If (in contrast) repetition is allowed (e.g. "AAA1X") then the answer changes to $$(36)^5.$$ – user2661923 Nov 05 '20 at 14:31