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?

Total balls = $4 + 5 + 6 = 15$ balls

Total ways to draw 2 balls = $^{15}C _2= 105$ ways

For one ball to be white:

White and Blue: $5 \times 4 = 20$ ways

White and Green: $5 \times 6 = 30$ ways

Total favorable outcomes = $20 + 30 = 50$ ways

Probability = $\frac{50}{105} = \frac{10}{21}$

Therefore, probability that one ball is white = $\frac{10}{21}$