A bag contains 2 red, 3 green and 2 blue balls. 2 balls are to be drawn randomly. What is the probability that the balls drawn contain no blue ball ?
Total number of balls = 2 + 3 + 2 = 7
Total number of outcomes = Drawing 2 balls out of 7
= $$C^7_2 = \frac{7 \times 6}{1 \times 2} = 21$$
Favourable outcomes = Drawing 2 balls out of 5 (so that none is blue)
= $$C^5_2 = \frac{5 \times 4}{1 \times 2} = 10$$
=> Required probability = $$\frac{10}{21}$$
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