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.

• A. 1000
• B. 2000
• C. 1200
• D. 1600

Answer 1

The correct option is B

2000

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 color. Here, 3 balls can be selected from 6 red balls ${}^6{C}_3$ in ways.

3 balls can be selected from 5 white balls ${}^5{C}_3$ in ways.

3 balls can be selected from 5 blue balls ${}^5{C}_3$ in ways.

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

${}^6{C}_3{\times }^5{C}_3$ ${}^5{C}_3$

= 2000