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.

Answer 1

Solution:
Two black balls can be selected out of 5 black balls in ⁵C₂ ways.Similarly, 3 red balls can be selected out of 6 red balls in ⁶C₃ ways.Therefore the number of ways in which 2 black balls and 3 red balls can be drawn is ⁵C₂ × ⁶C₃ . 
Now ⁵C₂ × ⁶C₁₃ 

= 

= 10 × 20 = 200
Thus, out of 5 black and 6 red balls, 2 black and 3 red balls can be selected in 200 ways.