We are to compute the probability that in 10 independent trials (simulations), exactly 3 distinct alleles among 6 are observed, where at each step, an allele is selected with probability proportional to its frequency (i.e., multinomial sampling without replacement — but since no actual frequencies are given, assume uniform distribution over alleles for symmetry). However, the problem states selected uniformly based on relative frequency, but without specific weights, and to make it solvable, we interpret that each allele has equal chance — or more naturally, that the selection is uniform over the 6 alleles at each step (i.e., discrete uniform).

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**Why Understanding Allele Diversity Matters in Everyday Choices** Recent discussions around biological sampling models have revealed surprising relevance in everyday decision-making. From product testing to trend forecasting, understanding how diversity emerges in repeated selections offers insight into probability, unpredictability, and outreach. One intriguing question involves computing the odds of observing exactly 3 distinct alleles among 6 in 10 independent trials—where each allele is chosen uniformly at random. While the sampling method defaults to equal likelihood, the underlying math reflects deeper patterns in randomness and diversity. --- **Understanding the Probability: What You’re Really Measuring**