Check sibling questions

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

Misc 2 - Chapter 16 Class 11 Probability - Part 2

This video is only available for Teachoo black users

Solve all your doubts with Teachoo Black (new monthly pack available now!)


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 = 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒘𝒂𝒚𝒔 𝒕𝒐 𝒔𝒆𝒍𝒆𝒄𝒕 𝟑 𝒅𝒊𝒂𝒎𝒐𝒏𝒅 × 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒘𝒂𝒚𝒔 𝒕𝒐 𝒔𝒆𝒍𝒆𝒄𝒕 𝟏 𝒔𝒑𝒂𝒅𝒆﷮𝑻𝒐𝒕𝒂𝒍 𝒘𝒂𝒚𝒔 𝒕𝒐 𝒔𝒆𝒍𝒆𝒄𝒕 𝟒 𝒄𝒂𝒓𝒅𝒔﷯ = 𝟏𝟑𝑪𝟑 × 𝟏𝟑𝑪𝟏﷮𝟓𝟐𝑪𝟒﷯ = 13!﷮3!(13 − 3)﷯ × 13!﷮1! 13 −1﷯!﷯﷮ 52!﷮4! 52 − 4﷯!﷯﷯ = 13!﷮3!10!﷯ × 13!﷮1!12!﷯﷮ 52!﷮4!48!﷯﷯ = 13!﷮3!10!﷯ × 13!﷮12!﷯ × 4!48!﷮52!﷯ = 286﷮20825﷯

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.