A bag contains 5 black and 6 red balls.
Question:

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.

Solution:

2 black and 3 red balls are to be selected from 5 black and 6 red balls.

Required number of ways $={ }^{5} C_{2} \times{ }^{6} C_{3}=\frac{5}{2} \times \frac{4}{1} \times \frac{6}{3} \times \frac{5}{2} \times \frac{4}{1}=200$