Question

In how many ways can $12$ balls divided between $2$ boys, one receiving $5$ and other $7$ balls?

• A. $1080$
• B. $1184$
• C. $1584$
• D. None of these

Answer 1

The correct option is C

$1584$

Explanation for the correct option:

Finding the number of ways of dividing the balls between the boys:

We can arrive at two cases from the given information

Case 1: the first boy receives $5$ ball and the second boy receives $7$ balls.

Case 2: the first boy receives $7$ ball and the second boy receives $5$ balls.

The number of ways that $12$ balls can be divided if one receiving $5$ and other $7$balls $=\frac{12!}{5!\times 7!}$

$$\begin{gathered} =\frac{12!}{5!\times 7!}\times 2 \\ =\frac{12\times 11\times 10\times 9\times 8\times 7!}{5\times 4\times 3\times 2\times 1\times 7!}\times 2 \\ =1584 \end{gathered}$$

Hence, option (C) is correct.