In a box of 12 pens, 4 are blue, 5 are black, and 3 are red. If you select 3 pens at random, what is the probability that you get pens of all different colors?

Instruction: Calculate the probability of selecting 3 pens, each of a different color, without replacement.

Context: This question evaluates the candidate's understanding of combinations and probability without replacement.

Updated

Official answer

There are C(12,3)=220 uniformly possible unordered selections of three distinct pens. For one pen of each color, choose one of four blue, one of five black and one of three red pens: 4×5×3=60 selections.

The probability is 60/220=3/11, about 27.27%.

Multiplying these choice counts is a counting principle; it does not make the successive random draws independent. A sequential check includes all six color orders: 6×(4/12)(5/11)(3/10)=3/11.

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