A bag contains 5 black and 6 red balls.Determine the number of ways in which 2 black and 3 red balls can be selected

Question

$\begin{array}{1 1}(A)\;100\\(B)\;300\\(C)\;400\\(D)\;200\end{array} $

Answer 1

Toolbox:

• $C(n,r)=\large\frac{n!}{r!(n-r)!}$

The number of ways in which 2 black balls out of 5 black balls are selected.

$5C_2$

The number of ways in which 3 red balls out of 6 red balls are selected.

$6C_3$

The number of ways in which 2 black and 3 red balls can be selected.

$\Rightarrow 5C_2\times 6C_3$

$\Rightarrow \large\frac{5\times 4}{1\times 2}\times \frac{6\times 5\times 4}{1\times 2\times 3}$

$\Rightarrow 10\times 20$

$\Rightarrow 200$

Hence (D) is the correct answer.