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# Magic trick probability

What is the probability that a King will be adjacent to an Ace in a well shuffled deck of 52 cards ?

Note by Shubham Raj
3 years, 10 months ago

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The problem has been solved here

The required probability is: $$\displaystyle 1- \dfrac{44!\cdot \sum_{k=1}^{3} \binom{3}{k-1}(4!) \binom{45}{k}\, (45-k)\, (46-k)\, (47-k)\, (48-k)}{52!} = \dfrac{284622747}{585307450} \approx 0.486279043603494$$ · 3 years, 10 months ago

First , you should clarify it. Do you mean a particular king will be adjacent to a particular ace or at least one king would be adjacent to an adjacent to at least one ace or a particular king would be adjacent to at least one ace or at least one king will be adjacent to a particular ace ? · 3 years, 10 months ago

Any king adjacent to any ace. · 3 years, 10 months ago

Probably, any king would be adjacent to any ace. · 3 years, 10 months ago