TxO Math Bowl 2024 - Team Contest - Problem 15

Let $n=\dfrac{(2^{11})!}{(2^6)!}$ and let $k$ be a randomly chosen positive factor of $n$ . The probability that $k$ is even can be expressed as $\frac{a}{b}$ , where $a$ and $b$ are relatively prime positive integers. Compute $a+b$ .

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Problem Tags: Counting and probability Number theory

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Category: TxO Math Bowl Team Contest
Points: 4
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