Question

Five cards are dealt from a standard 52-card deck (four suits of 13 cards each)    A) the number of possible hands i...


Five cards are dealt from a standard 52-card deck (four suits of 13 cards each) 

 

A) the number of possible hands is 2,598,960 explain how this number is obtained. Does this number represent permutations or combinations?

B) find the probability of being dealt a "flush" (all five cards the same suit) 

 

Answer

given

Five cards are dealt from a standard 52-card deck (four suits of 13 cards each) 

A)The
     number of possible 5-card hands isC52=52,598,960

B)If we pick the suit first, we have 4C1 = 4 choices. For that suit, there are 13 cards from which we choose 5. Thus, we have 13C5 = 1287 choices. Subtracting the straights, (which may start with ace, king, queen, ... 5), reduces this number by 10.  flushes= 4C1·(13C5  10)               = 4·1277                 = 5108 Dividing by the number of possible hands gives the probability:   flush  = 51082598960 =1.96510-3 

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