Example 17

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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 and C finish first second and third respectively Hence , L = {ABC} 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﷯