Question

Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls, and 5 blue balls if each selection consists of 3 balls of each color.

Answer 1

Given that,

We need to select the 3 red, 3 white, and 3 blue balls out of 6 red, 5 white and 5 blue balls. 

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

⇒ N = (no. of ways of selection of 3 red balls out of 6 red balls) × (no. of ways of selection of 3 white balls out of 5 white balls) × (no. of ways of selection of 3 blue balls out of 5 blue balls) 

⇒ N = (⁶C₃) × (⁵C₃) × (⁵C₃)

We know that,

ⁿC_r = \(\frac{n!}{(n-r)!r!}\)

And also,

n! = (n)(n – 1)......2.1

⇒ N = 20 × 10 × 10 

⇒ N = 2000 

∴ The no. of ways of selection is 2000.