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Difference between revisions of "2023 SSMO Team Round Problems/Problem 7"

(Created page with "==Problem== Let <math>S = \{1, 2, 3, 4, \cdots, 23\}</math> and let there be randomly chosen sets <math>A, B, C</math> where <math>A, B, C \subseteq S</math>. The probability...")
 
(No difference)

Latest revision as of 22:25, 15 December 2023

Problem

Let $S = \{1, 2, 3, 4, \cdots, 23\}$ and let there be randomly chosen sets $A, B, C$ where $A, B, C \subseteq S$. The probability that $|A| + |B| = |C|$ can be expressed as $\frac{m}{n}$. Let $2^a$ be the largest power of $2$ such $2^a \mid n$. Find $a$.

Solution

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