What is the probability that a five-card poker hand contains cards of five diffe

Anish Buchanan

Anish Buchanan

Answered question

2021-10-19

What is the probability that a five-card poker hand contains cards of five different kinds?

Answer & Explanation

tabuordg

tabuordg

Skilled2021-10-20Added 99 answers

Number of hands in total
The order of the cards does not matter and thus we need to use the definition of a combination.
A standard deck of cards contain 52 cards. A five -card poker hand selects 5 of the 52 cards
C(52,5)=52!5!(525)!=52!5!47!=2,598,960
Number of hands containing 5 different cards
We need to select 5 of the 13 denominators (kinds) and then 1 of the 4 cards is selected from each of the five denominations.
C(13,5)=13!5!(135)!=13!5!8!=1287
C(4,1)=4!1!(41)!=4!1!3!=4
Use the product rule:
128744444=128745=1,317,888
Result: 21124165

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