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

  1. Chapter 7 Class 11 Permutations and Combinations
  2. Serial order wise
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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 ๐‘›!/๐‘1!๐‘2!๐‘3! Here n = 9 Out of 9 discs, 4 red, 3 yellow and 2 green & p1 = 4, p2 = 3, p3 = 2 The number of arrangement = ๐‘›!/๐‘1!๐‘2!๐‘3! = 9!/(4! 3! 2!) = (9 ร— 8 ร— 7 ร— 6 ร— 5 ร— 4!)/(4! ร— (3 ร— 2 ร— 1)(2 ร— 1)) = (9 ร— 8 ร— 7 ร— 6 ร— 5)/(3 ร— 2 ร— 2) = 1260. Hence, total number of arrangements is 1260

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