<s>[INST] Card probability problem: Five cards will be dealt from a well-shuffled deck. Find the chance of getting an ace or a king among the 5 cards. Five cards will be dealt from a well-shuffled deck.
Find the chance of getting an ace or a king among the 5 cards.
I think question means getting at least a king or an ace, and here is my procedure:
$p$(an ace or a king among 5 cards)=$p$(at least an ace)+$p$(at least an king)-$p$(ace and king at the same time)
$p$(at least an ace)=$1-\frac{48}{52}\times\frac{47}{52}\times\frac{46}{52}\times\frac{45}{52}\times\frac{44}{52}$
$p$(at least an king)=$1-\frac{48}{52}\times\frac{47}{52}\times\frac{46}{52}\times\frac{45}{52}\times\frac{44}{52}$
$p$(ace and king at the same time)=...
Here I am stuck because there are many combination that ace and king are together. I feel like I misintepreted the question. Could someone give an insight?
 [/INST] Using 1 -
$$1 - \frac {\binom{44}{5} } { \binom{52}{5} } = 0.5821374704$$
Using 1 + 2 + 3 + 4 + 5 
$$\frac {\binom{8}{1} \binom{44}{4} + \binom{8}{2} \binom{44}{3} + \binom{8}{3} \binom{44}{2} + \binom{8}{4} \binom{44}{1}  + \binom{8}{5}} { \binom{52}{5} } = 0.5821374704$$ 
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