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

  • question_answer The number of different words that can be formed out of the letters of the word 'MORADABAD' taken four at a time is

    A) 500

    B) 600

    C) 620

    D) 626

    Correct Answer: D

    Solution :

    In MORADABAD, we have 6 different types of letters \[3{{A}^{s}}\],\[2{{D}^{s}}\] and rest four different. We have to form words of 4 letters. (i) All different \[^{6}{{P}_{4}}=6\times 5\times 4\times 3=360\]. (ii) Two different two alike \[^{2}{{C}_{1}}{{\times }^{5}}{{C}_{2}}\times \frac{4\ !}{2\,\,!}=240\] (iii) 3 alike 1 different \[^{1}{{C}_{1}}{{\times }^{5}}{{C}_{1}}\times \frac{4\ !}{3\ !}=20\] (iv) 2 alike of one type and 2 alike of other type \[^{2}{{C}_{2}}\times \frac{4\ !}{2\ !\ 2\ !}=6\] Therefore total number of words \[=360+240+20+6=626\].

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