SOLUTION: Given a standard deck of 52 cards with 5 cards being dealt to a player. (a)find the probability that the player hand will have all 5 cards as spades. (b)now find the probability

Question 766655: Given a standard deck of 52 cards with 5 cards being dealt to a player.
(a)find the probability that the player hand will have all 5 cards as spades.
(b)now find the probability that the player's hand is a flush. Note that a flush is a 5 card poker hand with all 5 cards being the same suit.
Found 2 solutions by DrBeeee, stanbon:
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
First we need to calculate how many 5 card hands that can be dealt from a standard 52 card deck. This is
(1) 52P5
However we don't care about the order of the 5 cards so we really want
(2) 52C5 = 52P5/5!
Now we need to determine how many of these hands can be all spades. Since there are 13 spades in the deck we can have
(3) 13P5 and again since order doesn't matter we want
(4) 13C5 = 13P5/5!
The probability of being dealt a spade flush is
(5) P(all spades) = 13P5/5!/(52P5/5!) or
(6) P(all spades) = 13P5/52P5 or
(7) P(all spades) = 13*12*11*10*9/(52*51*50*49*48) or after cancellations
(8) P(all spades) = 11*3/(4*17*5*49*4) or
(9) P(all spades) = 33/66640
Answer to a) is P(flush in spades) = 33/66640
For the second question, "any flush" is 4 times as probable than that of one of the four suits, therefore the
Answer to b) is P(flush in any suit) = 33/16660
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Given a standard deck of 52 cards with 5 cards being dealt to a player.
(a)find the probability that the player hand will have all 5 cards as spades.
# of ways to succeed: 13C5 = 1287
# of possible 5 card hands: 52C5
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P(5 spades) = 1287/52C5 = 0.000495..
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(b)now find the probability that the player's hand is a flush. Note that a flush is a 5 card poker hand with all 5 cards being the same suit.
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# of ways to get a flush in each suit:: 9
# of ways to get a flush in 4 suits:::: 36
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P(flush) = 36/52C5 = 0.0000139
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Cheers,
Stan H.
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