JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Critical Thinking Questions

  • question_answer The number of ways in which the letters of the word ARRANGE can be arranged such that both R do not come together is [MP PET 1993]

    A) 360

    B) 900

    C) 1260

    D) 1620

    Correct Answer: B

    Solution :

    The word ARRANGE, has AA, RR, NGE letters, that is two A' s, two R's and N, G, E one each. \[\therefore \] The total number of arrangements =\[\frac{7\,!}{2\,!\,2\,!\,1\,!\,1\,!\,1\,!}=1260\] But, the number of arrangements in which both RR are together as one unit = \[\frac{6\,!}{2\,!\,1\,!\,1\,!\,1\,!\,1\,!}=360\] \[\therefore \] The number of arrangements in which both RR do not come together  = 1260 - 360 = 900.

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