Question

A bag contains 6 white, 7 red and 5 blue balls. Three balls are drawn at random. Find the probability of the event 'balls drawn are one of each color'.

• A. 6/18
• B. 35/136
• C. 1/4
• D. 35/172

Answer 1

The correct option is B

35/136

Total number of balls = 6+7+5=18

Number of ways of choosing 3 balls =$18c_3$

Number of ways of choosing exactly one white ball =${}^6{c}_1$

Number of ways of choosing exactly one red ball =${}^7{c}_1$

Number of ways of choosing exactly one blue nall =${}^5{c}_1$

$\Rightarrow$ Number of ways of choosing 3 balls =${}^6{c}_1{\times }^7{c}_1{\times }^5{c}_1$ of one color each.

$\therefore$ Probability =$\frac{{}^6{c}_1{\times }^7{c}_1{\times }^5{c}_1}{{}^{18}{c}_3}=\frac{35}{136}$