A box contains 4 red balls, 3 blue balls, and 5 green balls. Three balls are drawn at random without replacement. What is the probability that all three balls are of different colors?
Show the answer and explanation
Correct answer
C. 3/11
Principle or equation
For drawing without replacement, the probability of a sequence of specific outcomes is the product of the probabilities at each draw, adjusting the total and favorable counts after each draw. For unordered selections, use combinations.
Why this answer is correct
Total balls = 4+3+5=12. We need one red, one blue, one green in any order. Number of favorable outcomes: choose 1 red from 4, 1 blue from 3, 1 green from 5: 4*3*5=60. Total ways to choose 3 balls from 12: C(12,3)=220. Probability = 60/220 = 3/11.
Example
If a bag has 2 red, 2 blue, 2 green, the probability of drawing one of each in 3 draws without replacement is (2*2*2)/C(6,3)=8/20=2/5.
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