JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Mock Test - Permutations and Combinations

  • question_answer
    Number of ways in which Rs. 18 can be distributed amongst four persons such that nobody receives less than Rs. 3 is

    A) \[{{4}^{2}}\]             

    B) \[{{2}^{4}}\]

    C) 4!                   

    D) none of these

    Correct Answer: D

    Solution :

    [d] Suppose \[{{i}^{th}}\]person receives Rs. \[{{x}_{i}};i=1,2,3,4\] Then,    \[{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+{{x}_{4}}=18,\]where \[{{x}_{i}}\ge 4\] Let \[{{y}_{i}}={{x}_{i}}-3,i=1,2,3,4.\]Then, \[{{y}_{1}}+{{y}_{2}}+{{y}_{3}}+{{y}_{4}}=6\] The total number of ways is equal to number of solutions of the above equation, which is given by \[^{6+4-1}{{C}_{4-1}}{{=}^{9}}{{C}_{3}}=84.\]

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