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JEE Main & Advanced Sample Paper JEE Main Sample Paper-7

  • question_answer
    Total number of ways in which 256 identical balls can be placed in '16' numbered boxes (1, 2, 3 ....16) such that \[{{r}^{th}}\] box contains at least ?r? \[\left( 1\le r\le 16 \right)\] balls is

    A)  \[^{120}{{C}_{15}}\]                      

    B)  \[^{135}{{C}_{15}}\]

    C)  \[^{256}{{C}_{15}}\]                      

    D)  \[^{255}{{C}_{15}}\]

    Correct Answer: B

    Solution :

    If we put minimum number of balls in each box, then remaining 256 - 136 = 120 identical balls can be put in \[^{120+16-1}{{C}_{16}}-1{{=}^{135}}{{C}_{15}}\] ways without restriction.


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