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

  • question_answer A library has \[a\] copies of one book, \[b\] copies of each of two books, \[c\] copies of each of three books and single copies of \[d\] books. The total number of ways in which these books can be distributed is

    A) \[\frac{(a+b+c+d)\ !}{a\ !\ b\ !\ c\ !}\]

    B) \[\frac{(a+2b+3c+d)\ !}{a\ !\ {{(b\ !)}^{2}}{{(c\ !)}^{3}}}\]

    C) \[\frac{(a+2b+3c+d)\ !}{a\ !\ b\ !\ c\ !}\]

    D) None of these

    Correct Answer: B

    Solution :

    Total number of books \[=a+2b+3c+d\] Since there are \[b\] copies of each of two books, \[c\] copies of each of three books and single copies of \[d\] books. Therefore the total number of arrangements is \[\frac{(a+2b+3c+d)\ !}{a\ !\ {{(b\ !)}^{2}}{{(c\ !)}^{3}}}\].


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