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Home » $$ \frac\sqrt5(\sqrt3 + \sqrt2)(\sqrt3 - \sqrt2)(\sqrt3 + \sqrt2) $$ - Appfinity Technologies

$$ \frac\sqrt5(\sqrt3 + \sqrt2)(\sqrt3 - \sqrt2)(\sqrt3 + \sqrt2) $$ - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 $ k = 6 $: $ \binom{6}{6} \cdot 0^{10} = 1 \cdot 0 = 0 $

📌 - 58593750 + 15728640 - 1180980 + 15360 - 6 = \boxed{2941680}

📌 Final Answer:** $ \boxed{2941680} $

📌 Question:** A stack of 12 distinct cards is shuffled and dealt into 3 equal piles of 4 cards each. What is the probability that a specific card (say, the Ace of Spades) ends up in the first pile?

📌 There are 12 distinct cards, and we deal them into 3 piles of 4 cards each.

📌 We fix the Ace of Spades and compute the probability it lands in the first pile.

📌 Since the deal is random and all card positions are equally likely, the Ace of Spades has an equal chance of being in any of the 12 positions.

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