A Royal Flush

Alex and Brian are playing a game of Poker. They are each dealt a hand of 5 cards from the same deck of cards.

Alex knows that there are only 4 Royal flushes (consisting of 10 , J , Q , K , A 10, J, Q, K, A of the same suit). Since there are ( 52 5 ) { 52 \choose 5 } ways to distribute the cards, so the probability of getting a Royal flush is P = 4 ( 52 5 ) P = \frac{ 4}{ { 52 \choose 5} } .

Brian revealed that he got a straight flush consisting of 5 , 6 , 7 , 8 , 9 5, 6, 7, 8, 9 of hearts.

What can we say about the probability that Alex has a Royal flush?

Equal to P P Less than P P Greater than P P

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