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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 39

  • question_answer
    Number of ways in which 13 identical apples can be distributed among 3 persons so that no two persons receive equal number of apples and each can receive none, one or more apples, is

    A) \[90\]                    

    B)        \[84\]

    C) \[105\]                   

    D)        \[14\]

    Correct Answer: B

    Solution :

    [b] Total number of ways of distribution without any restriction \[{{=}^{13+3-1}}{{C}_{3-1}}{{=}^{15}}{{C}_{2}}=105\] But it will also contain the ways when exactly two persons receive equal number of apples. Following are the possible cases:
    0 0 13
    1 1 11
    . . .
    . . .
    . . .
    6 6 1
    Number of ways \[=7\times 3=21\] \[\therefore \] Required number of ways \[=105-21=84\]


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