- 58593750 + 15728640 - 1180980 + 15360 - 6 = \boxed{2941680}
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- $ k = 5 $: $ -\binom{6}{5} \cdot 1^{10} = -6 \cdot 1 = -6 $
- $ k = 6 $: $ \binom{6}{6} \cdot 0^{10} = 1 \cdot 0 = 0 $
- Now sum:
- 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.
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