I'm stumped on this recreational problem: How many 5-digit numbers are there such that every next digit is smaller than the previous one?
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Originally Posted by elninio I'm stumped on this recreational problem: How many 5-digit numbers are there such that every next digit is smaller than the previous one? $\displaystyle \binom{10}{5}$
Last edited by Plato; Sep 30th 2009 at 08:32 AM.
Hmm, I didnt think it would be that simple!
Originally Posted by elninio Hmm, I didnt think it would be that simple! Well give me any subset of five digits. Say $\displaystyle \{3,9,0,7,4\}$. Arrange is desending order: $\displaystyle 97430$. That's sort of number described. So it is just the number of five element subsets of the digits.
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