Miscellaneous

Chapter 14 Class 11 Probability
Serial order wise

### 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﷯

Made by

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.