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From a deck of cards you draw 5 cards without replacement. What is the probability of drawing: * 5 spades * 3 Aces * 2 jacks and 3 aces * 2 fives 2 nines and 1 ace Solution five spades =13P5/52P5 =(13*12*11*10*9)/(52*51*50*49*48) =0.0004952 ( answer) 3 aces = 5C2*4P3 *48P2/(52P5) =(5*2*4*3*2*48*47)/(52*51*50*49*48) =0.0017361 ( answer) 2 jacks and 3 aces =5C2*4P2*4P3/(52P5) = (5*2*4*3*4*3*2)/(52*51*50*49*48) =0.0000092345 ( answer) 2 fives 2 nines 1 ace =5C3*4P2*4P2*4P1/(52P5) = (5*2*4*3*4*3*4)/(52*51*50*49*48) =0.0000185 (answer).

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- From a deck of cards you draw 5 cards without replacement. What is the probability of drawing: * 5 spades * 3 Aces * 2 jacks and 3 aces * 2 fives 2 nines and 1 ace Solution five spades =13P5/52P5 =(13*12*11*10*9)/(52*51*50*49*48) =0.0004952 ( answer) 3 aces = 5C2*4P3 *48P2/(52P5) =(5*2*4*3*2*48*47)/(52*51*50*49*48) =0.0017361 ( answer) 2 jacks and 3 aces =5C2*4P2*4P3/(52P5) = (5*2*4*3*4*3*2)/(52*51*50*49*48) =0.0000092345 ( answer) 2 fives 2 nines 1 ace =5C3*4P2*4P2*4P1/(52P5) = (5*2*4*3*4*3*4)/(52*51*50*49*48) =0.0000185 (answer)

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