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?

The total number of balls in the bag is 7, making the total ways to draw two balls 7C2, which is 21. Since we want none of the drawn balls to be blue, we must select both balls from the 5 non-blue balls (2 red and 3 green). The number of ways to choose 2 balls from these 5 is 5C2, which is 10. The required probability is 10/21.

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