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

Answer : There are 5 black and 6 red balls. So,

The number of ways of selecting 2 black balls from 5 black balls is ⁵C2, and number of ways of selecting 3 red balls from 6 red balls is ⁶C3.

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

⁵C2 × ⁶C3 ways.

⇒200 ways

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