Question

$9$ 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 equal to:

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

Answer 1

The correct option is C

$17280$

Find the number of ways of arranging one ball in each of the boxes:

Given:

$9$ balls are to be placed in $9$ boxes and $5$ of the balls cannot fit into $3$ small boxes.

$\therefore$The number of ways of arranging one ball in each of the boxes $={}^{6}P_5\times 4!$

$$\begin{gathered} =720\times 24 \\ =17280 \end{gathered}$$ $\left[\mathbf{\because }{}^{\mathbf{n}}\mathit{P}_{\mathbf{r}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{n}\mathbf{!}}{\left(n-r\right)\mathbf{!}}\right]$

Hence, Option ‘C’ is Correct.