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?

Solution (By Examveda Team)

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
$$\eqalign{ & = \frac{{5 \times 4}}{{{}^9{C_2}}} \cr & = \frac{{20}}{{36}} \cr & = \frac{5}{9} \cr} $$