Question

Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 4 blue balls if each selection consists of 3 balls of each color

Answer 1

Number of ways of selecting 3 red balls from 6 red balls:

$$\frac{6!}{3!(6-3)!}=20$$

Number of ways of selecting 3 white balls from 5 white balls:

$$\frac{5!}{3!(5-3)!}=10$$

Number of ways of selecting 3 blue balls from 4 blue balls:

$$\frac{4!}{3!(4-3)!}=4$$

So,

$$N=(20)(10)(4)=800$$