Question: A virologist has 6 samples: 2 from virus strain A, 2 from strain B, and 2 from strain C. She randomly selects 4 samples to test. What is the probability that she selects exactly one sample from each strain? - Sterling Industries

Understanding the Context

Why This Query Resonates in US Scientific and Public Discussions

Recent trends in virology labs emphasize transparency, accuracy, and risk-aware protocols. As new variants emerge globally, researchers rigorously manage sample integrity to avoid contamination and bias. Sampling strategies directly affect data reliability—and thus public health responses. The question appears at the intersection of advanced mathematics and applied lab science, a niche gaining momentum in podcasts, science communication, and educational platforms. Audiences increasingly seek clear explanations of how such calculations influence testing protocols, trial outcomes, and policy trust. This query positions itself at that nexus—accessible, relevant, and aligned with clear information needs.

Understanding the Math Behind the Probability

Let’s unpack how probability unfolds in this scenario. The lab chooses 4 out of 6 total samples. Each strain—A, B, and C—has 2 specimens. We want exactly one sample from each strain in those 4 draws. Since two samples remain after choosing one from each strain, the fourth sample must come from any strain, but in this case, that fifth selection isn’t allowed—so only exact one-per-strain combinations count.

Key Insights

First, total ways to choose 4 samples from 6 is given by the combination formula:
C(6,4) = 15

Now, count favorable outcomes: choosing one sample from each strain, plus one additional sample that does not create duplicate strains. But wait—since each strain only has 2 samples and we’re picking only one per strain, the only way to satisfy “exactly one from each strain” is to pick one from A, one from B, one from C, and then one more—but that automatically creates at least one duplicate strain. So the correct interpretation is: exactly one full set across all three strains, meaning one A, one B, one C, and no extra from any. That requires exactly three samples, but the selection is four.

Therefore, we’re calculating: Probability of selecting one sample from each strain, with no strain overrepresented, but since only four are chosen, exactly one strain must be missing—however, the original question asks for exactly one from each strain in 4 draws, which is only possible if that fourth sample belongs uniquely to a third strain but counts only once—immission.

The precise interpretation: To select exactly one sample from each strain in four total samples means choosing precisely one from A, one from B, one from C—and since there’s no fourth sample from a new strain, the fourth must be duplicate—but that violates “exactly one per strain.” So the correct frame is: choosing exactly one sample per strain from the four total, meaning all four are distinct strain representations—but with only three strains, this is impossible without repeating.

But wait—since we select 4, and have 3 strains, by pigeonhole principle, at least one strain is represented twice. So “exactly one from each strain” in 4 samples is mathematically impossible unless overlap excluded—but with only three strains, four samples imply at least one repetition.

Final Thoughts

Thus, the event is impossible—probability zero—but that’s not what readers want to learn.

The intended meaning is clearer: What is the chance she selects exactly one sample from each of the three strains, given the fixed supply—implying one full sample from A, one from B, one from C, and the fourth being irrelevant to strain count. But strictly speaking, the fourth sample belongs to one of the three strains. So “exactly one per strain” in four selections equates to choosing one from each strain and one extra—so total distribution becomes 2-1-1.

Hence, correct phrasing: The probability that among 4 randomly selected samples from 2A, 2B, 2C, she ends up with exactly one sample from strain A, exactly one from B, exactly one from C—and the fourth sample from any, but since only 6 total, and 2+2+2=6, selecting 4 leaves 2 unused, but the selection includes