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Misc 11 - In how many ways can letters of ASSASSINATION - Permutation- repeating

  1. Class 11
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Misc, 11 In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together? Since we need to assigned 4S together 4S consider as one block Remaining letters are A, A, I, N, A, T, I, O, N Since letters are repeating Hence we use this formula = 𝑛!﷮𝑝1!𝑝2!𝑝3! ﷯ Hence n = Letters to be arranged = 9 + 1 = 10 Since 3A, 2I, 2N p1 = 3, p2 = 2, p3 = 2, Number of arrangements where the S’s are together = 10!﷮3!2!2!﷯ = 10×9×8×7×6×5×4×3!﷮3!×2×1×2×1﷯ = 151200 words

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
  • Ramnik Singh's image

    5 questions, either true or false. No student answer correctly and no students given same sequence of answers. How many total students.

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