Question

Three balls are to be picked from a bag containing 6 black, 5 white and 4 red balls. What is the probability that all the three balls are of different colour?

• A. $\frac{25}{91}$
• B. $\frac{22}{91}$
• C. $\frac{24}{91}$
• D. $\frac{26}{91}$

Answer 1

The correct option is C

$\frac{24}{91}$

Probability = $\frac{\left(Sumoffavourableoutcomes\right)}{\left(Sumoftotaloutcomes\right)}$
Probability that the three balls are of different colour,
$P=\left(\frac{6_{C_1}+5_{C_1}+4_{C_1}}{{15}_{C_3}}\right)\to P=\frac{(6\times 5\times 4)}{\left(\frac{15\times 14\times 13}{3\times 2\times 1}\right)}\to P=\left(\frac{24}{91}\right)$