A bag consists of 2 red balls, 3 green balls and 4 blue balls. In how many ways can 3 balls be drawn, if at least one of them is a blue ball?

A bag consists of 2 red balls, 3 green balls and 4 blue balls. In how many ways can 3 balls be drawn, if at least one of them is a blue ball? Correct Answer 74

There are 2 red balls, 3 green balls and 4 blue balls. The possible outcomes for at least one blue ball, when 3 balls are drawn from the bag are: (1 red, 1 green, 1 blue), (1 red, 2 blue), (1 green, 2 blue), (2 red, 1 blue), (2 green, 1 blue), (3 blue). Required number of ways = (2C1 * 3C1 * 4C1) + (2C1 * 4C2) + (3C1 * 4C2) + (2C2 * 4C1) + (3C2 * 4C1) + (4C3). ⟹ (2 * 3 * 4) + (2 * 6) + (3 * 6) + (1 * 4) + (3 * 4) + (4) ⟹ 24 + 12 + 18 + 4 + 12 + 4 = 74 Number of ways if at least one of them is blue = 74.
Bissoy MCQ

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