If $12$ identical balls are to be placed in $3$ identical boxes, then the probability that one of the boxes contains exactly $3$ balls is :

  • [JEE MAIN 2015]
  • A

    $22{\left( {\frac{1}{3}} \right)^{11}}$

  • B

    $\frac{{55}}{3}{\left( {\frac{2}{3}} \right)^{11}}$

  • C

    $55{\left( {\frac{2}{3}} \right)^{10}}$

  • D

    $220{\left( {\frac{1}{3}} \right)^{12}}$

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  • [IIT 2004]