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,
nCr = \(\frac{n!}{(n-r)!r!}\)
And also,
n! = (n)(n – 1)......2.1
⇒ N = 20 × 10 × 10
⇒ N = 2000
∴ The no. of ways of selection is 2000.