AoPS Wiki talk:Problem of the Day/July 15, 2011

Revision as of 03:51, 18 August 2011 by Neutrinonerd3333 (talk | contribs) (solution)

Problem

AoPSWiki:Problem of the Day/July 15, 2011

Solution

There are $\binom{10}{6}+\binom{10}{7}+\binom{10}{8}+\binom{10}{9}+\binom{10}{10}$ ways to satisfy the baby storks, out of a total of $2^10$ ways to catch the fish. Using the fact that $\binom{n}{k}=\binom{n}{n-k}$, we can quickly evaluate the probability as $\frac{270+120+45+10+1}{1024}=\frac{446}{1024}=\boxed{\frac{223}{512}}.

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