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Misc 2 - 4 cards are drawn. What is the probability - Using combination

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  1. Chapter 16 Class 11 Probability
  2. Serial order wise
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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 = ๐‘ต๐’–๐’Ž๐’ƒ๐’†๐’“ ๐’๐’‡ ๐’˜๐’‚๐’š๐’” ๐’•๐’ ๐’”๐’†๐’๐’†๐’„๐’• ๐Ÿ‘ ๐’…๐’Š๐’‚๐’Ž๐’๐’๐’… ร— ๐‘ต๐’–๐’Ž๐’ƒ๐’†๐’“ ๐’๐’‡ ๐’˜๐’‚๐’š๐’” ๐’•๐’ ๐’”๐’†๐’๐’†๐’„๐’• ๐Ÿ ๐’”๐’‘๐’‚๐’…๐’†๏ทฎ๐‘ป๐’๐’•๐’‚๐’ ๐’˜๐’‚๐’š๐’” ๐’•๐’ ๐’”๐’†๐’๐’†๐’„๐’• ๐Ÿ’ ๐’„๐’‚๐’“๐’…๐’”๏ทฏ = ๐Ÿ๐Ÿ‘๐‘ช๐Ÿ‘ ร— ๐Ÿ๐Ÿ‘๐‘ช๐Ÿ๏ทฎ๐Ÿ“๐Ÿ๐‘ช๐Ÿ’๏ทฏ = 13!๏ทฎ3!(13 โˆ’ 3)๏ทฏ ร— 13!๏ทฎ1! 13 โˆ’1๏ทฏ!๏ทฏ๏ทฎ 52!๏ทฎ4! 52 โˆ’ 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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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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