A bag contains 4 blue, 5 white and 6 green balls. Two balls are drawn at random. What is the probability that one ball is white?

We are given 4 blue balls 5 white balls and 6 green balls

Total balls = 4 + 5 + 6 = 15 balls

We are drawing 2 balls at random, and we need to find the probability that exactly one of them is white.

So, total ways  $$ = \binom{15}{2} = \frac{15 \times 14}{2} = 105 $$

We want one white ball and one non-white ball (i.e., either blue or green).

Number of ways to choose 1 white ball = $$ \binom{5}{1} = 5$$

Number of ways to choose 1 non-white ball = $$ \binom{10}{1} = 10 $$ (since 4 blue + 6 green = 10)

Favorable outcomes= $$ 5 \times 10 = 50 $$

So, Probability $$= \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{50}{105} = \frac{10}{21} $$