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 are yellow?

Answer: Option B

Number of red balls = 4
Number of yellow balls = 5
Number of pink balls = 6
Total balls = 4 + 5 + 6 = 15
Total possible outcomes = selection of 2 balls out of 15 balls
= $${}^{15}{C}_2$$  
=$$\frac{15!}{2!(15-2)!}$$
=$$\frac{15!}{2!\times 13!}$$
=$$\frac{15\times 14}{1\times 2}$$
=105
Total favourable outcomes = selection of 2 balls out of 4 orange and 6 pink balls.
$$={}^{10}{C}_2$$
= $$\frac{10!}{2!(10-2)!}$$
= $$\frac{10!}{2!\times 8!}$$
= $$\frac{10\times 9}{1\times 2}$$
= 45
∴ Required probability = $$\frac{45}{105}$$ = $$\frac{3}{7}$$