Example 17 - In a relay race there are five teams A, B, C, D, E

Example  17 - Chapter 16 Class 11 Probability - Part 2
Example  17 - Chapter 16 Class 11 Probability - Part 3

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Example 17 In a relay race there are five teams A, B, C, D and E. (a) What is the probability that A, B and C finish first, second and third, respectively. 3 teams will win from 5 teams Hence Total number of orders = 5P3 = 5!/(5 − 3)! = 5!/2! = (5 × 4 × 3 × 2!)/2! = 60 So, n(S) = 60 Let L be the event that A, B & C finish first second & third respectively Hence , L = {ABC} So, n(L) = 1 So, P(L) = (𝑛(𝐿))/(𝑛(𝑆)) = 𝟏/𝟔𝟎 Example 17 In a relay race there are five teams A, B, C, D and E. (b) What is the probability that A, B and C are first three to finish (in any order) (Assume that all finishing orders are equally likely) Let M be the event that A, B and C are first three in any order M = {ABC, ACB, BAC, BCA, CAB, CBA} Hence n(M) = 6 P(M) = (𝑛(𝑀))/(𝑛(𝑆)) = 6/60 = 𝟏/𝟏𝟎

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.