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Sagot :
The probability that a five-card hand will contain a straight = 5/1274
There are 52 cards in a deck from which each 13 cards are from 4 different suits (clubs, diamonds, spades and hearts) in a game of poker.
Each 13 cards from high to low are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. So a straight of five cards, i.e., five cards in unbroken numerical sequence would be got only from 10 cards in a sequence.
So the possible ways to get a single straight five from all four suits = [tex]4^5[/tex]
Now as we doesn't need all 5 cards from a single suit, we can ignore 4 ways from the above number. i.e., [tex]4^5-4 = 1020[/tex] ways.
Hence the possible ways to get a straight five from 10 cards from all four suits = 10 x 1020 = 10200 ways
Total number of ways to select 5 cards from 52 cards = 52C5
Thus,
The probability that a five-card hand will contain a straight = 10200 / 52C5
= 5/1274 Learn more about probability at https://brainly.com/question/5858025
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