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 colour.

Answer 1

There are a total of 6 red balls, 5 white balls, and 5 blue balls.

9 balls have to be selected in such a way that each selection consists of 3 balls of each colour.

Here,

3 balls can be selected from 6 red balls in ⁶C₃ ways.

3 balls can be selected from 5 white balls in ⁵C₃ ways.

3 balls can be selected from 5 blue balls in ⁵C₃ ways.

Thus, by multiplication principle, required number of ways of selecting 9 balls

^{= 6}C₃ x ⁵C₃ x ⁵C₃ = `(6!)/(3!3!) xx (5!)/(3!2!) xx (5!)/(3!2!)`

= `(6 xx 5 xx 4 xx 3!)/(3! xx 3 xx 2) xx (5 xx 4 xx 3!)/(3! xx 2 xx 1) xx (5 xx 4 xx 3!)/ (3! xx 2 xx 1`

= 20 x 10 x 10

= 2000