A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?

Answer: Option B

Two balls can be picked from nine balls in $${}^9{C}_2$$ ways.
We select one white ball and one red ball from five white balls and four red balls.
This can be done $${}^5{C}_1$$ . $${}^4{C}_1$$ ways.
∴ The required probability
$$\begin{array}{rl}& =\frac{5\times 4}{{}^9{C}_2}\\ & =\frac{20}{36}\\ & =\frac{5}{9}\end{array}$$