A bag contains 4 red, 5 yellow and 6 pink balls. Two balls are drawn at random. What is the probability that none of the balls drawn is yellow in colour?

Number of red balls = 4
Number of yellow ball = 5
Number of pink ball = 6
Total number of balls = 4 + 5 + 6 = 15
Total possible outcomes = selection of 2 balls out of 15 balls = ¹⁵C₂
= 15!/2!(15 - 2)!
= 15!/(2! × 13!)
= (15 × 14)/(1 × 2)
= 105.
Total favourable outcomes = selection of 2 balls out of 4 orange and 6 pink balls.
¹⁰C₂
= 10!/2!(10 - 2)!
= 10!/2!8!
= (10 × 9)/(1 × 2)
= 45.
∴ Required Probability = 45/105
= 3/7