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2024 SSMO Team Round Problems/Problem 13

Revision as of 15:45, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== In a deck of 54 cards (2 identical jokers, 4 identical cards with <math>1,2,3,\dots,13</math>), each card is dealt to one of 3 people, each having a <math>\frac{1...")
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Problem

In a deck of 54 cards (2 identical jokers, 4 identical cards with $1,2,3,\dots,13$), each card is dealt to one of 3 people, each having a $\frac{1}{3}$ chance of receiving each card. If the expected sum of the number of unique cards the three of them have can be expressed as $\frac{m}{n}$ for relatively prime positive integers $m$ and $n,$ find $m+n.$

Solution

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