Question
A box contains 8 red, 5 green, and 7 blue balls. Two
balls are drawn at random without replacement. What is the probability that both balls drawn are of different colors?Solution
Total number of balls = 8 + 5 + 7 = 20. The total number of ways to choose 2 balls from 20 is: C(20, 2) = (20 × 19) / 2 = 190. Now, the number of ways to choose 2 balls of different colors: Red and Green: 8 × 5 = 40 Red and Blue: 8 × 7 = 56 Green and Blue: 5 × 7 = 35 So, the total number of ways to choose 2 balls of different colors = 40 + 56 + 35 = 131. Therefore, the probability is: P(different colors) = 131 / 190 Correct Option: a)
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