Discussion
Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all the three balls are red is
Answer: B
The probability is 1/55.
There are 12 balls, 4 of them red, and the draws are without replacement:
\[ \begin{aligned} P &= \frac{4}{12} \times \frac{3}{11} \times \frac{2}{10} \\ &= \frac{24}{1320} = \frac{1}{55} \end{aligned} \]
The same answer comes from combinations: \(\binom{4}{3}/\binom{12}{3} = 4/220\). 1/27 is \((1/3)^{3}\), the answer with replacement. 1/36 and 1/72 come from other slips in the counting.
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