A bag contains 5 black and 6 red balls.

There are 5 black and 6 red balls. So,

The number of ways of selecting 2 black balls from 5 black balls is ${ }^{5} \mathrm{C} 2$, and number of ways of selecting 3 red balls from 6 red balls is ${ }^{6} C_{3}$.

Thus using the multiplication principle, the total number of ways will be

$\Rightarrow{ }^{5} \mathrm{C}_{2} \times{ }^{6} \mathrm{C}_{3}$ ways.

Applying ${ }^{n} C_{r}=\frac{n !}{r !(n-r) !}$

⇒200 ways

Thus, the total number of ways in which 2 black and 3 red balls can be selected is 200.