Question

$9$ different 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 :

• A. $18720$
• B. $18270$
• C. $17280$
• D. $12780$

Answer 1

The correct option is C $17280$

Out of the $9$ different balls, $5$ can not fit into $3$ small boxes.

So, those $5$ balls should be arranged in the remaining $6$ boxes.

$5$ different balls can be placed in $6$ boxes in ${}^6{P}_5$ ways$=\frac{6!}{1!}=720$ ways.
Now the remaining $4$ balls can be placed in $4$ remaining boxes in $4!=24$ ways.

So, using multiplication principle, the total number of ways of arranging is equal to $720\times 24=17280$.