## Problem of the Day #273: Count the Factors of TwoDecember 17, 2011

Posted by Saketh in : potd , trackback

One day, Alex erroneously simplifies $\frac{(2n)!}{n!}$ to $2!$, concluding that the fraction has exactly $1$ factor of $2$. In terms of $n$, how many does it really have? You may not use the floor function (or anything equivalent) in your answer.