9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of…

9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of arranging one ball in each of the boxes is
  1. $18720$
  2. $18270$
  3. $17280$
  4. $12780$

Solution

Required number of arrangements $ \begin{aligned} & ={ }^6 P_5 \times 4 ! \\ & =720 \times 24 \\ & =17280 \end{aligned} $

Asked in: AP EAMCET 2008

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