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Last updated at Feb. 10, 2020 by Teachoo
Transcript
Misc 2 4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade? Total 4 cards are to be selected out of 52 cards Hence Total ways to select 4 cards = 52C4 We need to select 3 diamond card & 1 spade card Total number of diamond card = 13 Number of diamond card to be selected = 3 Total ways to select 3 diamond card = 13C3 Also, Total number of spade card = 13 Number of spade card to be selected = 1 Total ways to select 1 spade card = 13C1 Hence, Probability of obtaining 3 diamonds and one spade = ๐ต๐๐๐๐๐ ๐๐ ๐๐๐๐ ๐๐ ๐๐๐๐๐๐ ๐ ๐ ๐๐๐๐๐๐ ร ๐ต๐๐๐๐๐ ๐๐ ๐๐๐๐ ๐๐ ๐๐๐๐๐๐ ๐ ๐๐๐๐ ๐๏ทฎ๐ป๐๐๐๐ ๐๐๐๐ ๐๐ ๐๐๐๐๐๐ ๐ ๐๐๐๐ ๐๏ทฏ = ๐๐๐ช๐ ร ๐๐๐ช๐๏ทฎ๐๐๐ช๐๏ทฏ = 13!๏ทฎ3!(13 โ 3)๏ทฏ ร 13!๏ทฎ1! 13 โ1๏ทฏ!๏ทฏ๏ทฎ 52!๏ทฎ4! 52 โ 4๏ทฏ!๏ทฏ๏ทฏ = 13!๏ทฎ3!10!๏ทฏ ร 13!๏ทฎ1!12!๏ทฏ๏ทฎ 52!๏ทฎ4!48!๏ทฏ๏ทฏ = 13!๏ทฎ3!10!๏ทฏ ร 13!๏ทฎ12!๏ทฏ ร 4!48!๏ทฎ52!๏ทฏ = 286๏ทฎ20825๏ทฏ
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