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Misc 5 - Out of 100 students, two sections of 40, 60 are formed - Using combination

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  1. Chapter 16 Class 11 Probability
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Misc 5 Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that • you both enter the same sections? n(S) = 100C40, n(A) = 98C38 P(A) = 𝑛(𝐴)﷮𝑛(𝑆)﷯ = 𝟗𝟖𝑪𝟑𝟖﷮𝟏𝟎𝟎𝑪𝟒𝟎﷯ = 98C38 ÷ 100C40 = 98!﷮38! 98 −38﷯!﷯ × 100!﷮40! 100 − 40﷯!﷯ = 98!﷮38!60!﷯ ÷ 100!﷮40!60!﷯ = 98!﷮38!60!﷯ × 40!60!﷮100!﷯ = 98! × 40! × 60!﷮38! × 60! × 100!﷯ = 40 × 39﷮100 × 99﷯ Probability that two students enter same section = Probability that both enter Section A + Probability that both enter Section B = P(A) + P(B) = 40 × 39﷮100 × 99﷯ + 60 × 59﷮100 × 99﷯ = 1560﷮9900﷯ + 3540﷮9900﷯ = 156﷮990﷯ + 354﷮990﷯ = 156 + 354﷮990﷯ = 510﷮990﷯ = 51﷮99﷯ = 𝟏𝟕﷮𝟑𝟑﷯ Misc 5 Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that (b) you both enter the different sections? Probability that they enter different section = 1 – Probability that both enter in same section = 1 – 17﷮33﷯ = 33 − 17﷮33﷯ = 𝟏𝟔﷮𝟑𝟑﷯

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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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