Question

A bag contains 5 blue and 4 black balls. Three balls are drawn at random. What is the probability that 2 are blue and 1 is black?

• A. $\frac{1}{3}$
• B. $\frac{2}{5}$
• C. $\frac{1}{6}$
• D. none

Answer 1

The correct option is D none

Number of ways of selecting 3 balls out of 9 $={}^9{C}_3$

Number of ways of selecting 2 blue balls out of 5 $={}^5{C}_2$

Number of ways of selecting 1 black ball out of 4 $={}^4{C}_1$

$P=\frac{{}^5{C}_2{\times }^4{C}_1}{{}^9{C}_3}$