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Example 9 - Find number of permutations of ALLAHABAD - Permutation- repeating

  1. Chapter 7 Class 11th Permutations and Combinations
  2. Serial order wise
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Transcript

Example 9 Find the number of permutations of the letters of the word ALLAHABAD. In ALLAHABAD There are 4A , 2L , 1H, 1B & 1D Since alphabets are repeating we will us this formula 𝑛!/𝑝1!𝑝2!𝑝3! Total number of alphabets = 9 Here n = 9 , There are 4A’s, 2L’s hence taking p1 = 4 & p2 = 2 Hence total number of permutation = 𝑛!/𝑝1!𝑝2! = 9!/4!2! = (9 Γ— 8 Γ— 7 Γ— 6 Γ— 5Γ— 4!)/((2 Γ— 1) Γ— 4!) = (9 Γ— 8 Γ— 7 Γ— 6 Γ— 5 )/2 = 7560

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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 contact him here.
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