Example 15 - In how many ways can 4 red, 3 yellow, 2 green discs - Permutation- repeating

Example 15 - Chapter 7 Class 11 Permutations and Combinations - Part 2

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Example 15 In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable ? Total number of discs = 4 red + 3yellow + 2 green n = 9. Since color are repeating so we use this formula 𝑛!/𝑝1!𝑝2!𝑝3! Here n = 9 Out of 9 discs, 4 red, 3 yellow and 2 green & p1 = 4, p2 = 3, p3 = 2 The number of arrangement = 𝑛!/𝑝1!𝑝2!𝑝3! = 9!/(4! 3! 2!) = (9 × 8 × 7 × 6 × 5 × 4!)/(4! × (3 × 2 × 1)(2 × 1)) = (9 × 8 × 7 × 6 × 5)/(3 × 2 × 2) = 1260. Hence, total number of arrangements is 1260

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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.