A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

Total number of balls
= (2 + 3 + 2)
= 7
Let S be the sample space
Then, n(S) = Number of ways of drawing 2 balls out of 7
n(S) = ⁷C₂
n(S) = (7×6)/(2×1)
n(S) = 21
Let E = Event of 2 balls, none of which is blue
∴ n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls
n(E) = ⁵C₂
n(E) = (5×4)/(2×1)
n(E) = 10
∴P(E) = n(E)/n(S)
=10/21