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A poker deck consists of cards ranked 2,3,4,5,6,7,8,9,10,J,Q,K,A, (13 different ranks) each in four suits, for a total of 52 distinct cards. A pinochle deck consists of two copies each of cards ranked 9,10,J,Q,K,A, each in four suits, for a total of 48 cards (24 pairs of identical cards).What is the probability that a five-card poker hand drawn from a pinochle deck contains no duplicate cards?

 Feb 15, 2020
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Pick a card any card.  Probability of this is 1.

 

Now pick a card not duplicate to the first card.  Probability of this is 46/47

 

Continuing we have

 

\(p=1 \dfrac{46}{47}\dfrac{44}{46}\dfrac{42}{45} \dfrac{40}{44} = \dfrac{112}{141}\)

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 Feb 16, 2020

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