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

Ways to select 2 balls out of 5 black balls = 5C2

Ways to select 3 balls out of 6 red balls = 6C3

Total ways of selecting 2 black and 3 red balls out of 5 black and 6 red balls.

=⁵C₂ × ⁶C₃

= ${\displaystyle \frac{5!}{2!3!}\times \frac{6!}{3!3!}}$

= ${\displaystyle \frac{5\times 4}{2}\times \frac{6\times 5\times 4}{3\times 2\times 1}}$

= 10 x 20

= 200