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
1. 18720
2. 18270
3. 17280
4. 12780

Answer 1

Correct Answer - Option 3 : 17280

Concept:

Number of ways of arranging n identical items in r ways is given  \({}_{r}^{n}P=\frac{n!}{\left( n-r \right)!}\)

Calculation:

Total number of balls are 9, and total number of boxes are also 9

5 balls cannot fit into 3 small boxes, this means that these 5 balls can only fit into 6 remaining balls.

so number of ways of arranging 5 balls in 6 boxes is:

 \(\begin{align} & _{5}^{6}P=\frac{\left( 6 \right)!}{\left( 6-5 \right)!} \\ & =6! \\ \end{align} \)

= 720 ways

Now, remaining 4 balls fits into 4 remaining boxes.

Number of ways of arranging 4 balls in 4 boxes is 4! = 24 ways

So total number of ways is 720 × 24 = 17280