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.

Question

Philoid · Accepted Answer

Given that we need to draw 2 black and 3 red balls from a bag of 5 black and 6 red balls.

Let us assume the no. of ways of drawing be N.

⇒ N = (no. of ways of selecting 2 black balls from 5 black balls) × (no. of ways of selecting 3 red balls from 6 red balls)

⇒ N = (⁵C₂) × (⁶C₃)

We know that ,

And also n! = (n)(n – 1)......2.1

⇒

⇒ N = 10 × 20

⇒ N = 200

∴ The no. of ways of drawing 2 black and 3 red balls is 200.