A space agriculture designer is configuring a seed dispenser that randomly selects one of 8 plant varieties each time it activates. If the dispenser operates 5 times independently, what is the probability that exactly two different varieties are selected, with one appearing exactly three times?

Sat, 02 May 2026 16:07:14 +0000

**Curious About Space Farming? This Seed Dispenser Puzzle Might Surprise You**
In an era where innovative agriculture solutions — from vertical farms to extraterrestrial crops — capture public imagination, a simple yet intriguing challenge has emerged among space agriculture designers. Imagine a compact seed dispenser programmed to randomly select from eight distinct plant varieties each time it activates. When operated five times independently, users often wonder: what’s the chance that exactly two varieties appear, with one chosen exactly three times? This isn’t hypothetical — it reflects real design patterns in automated urban farming systems aiming for biodiversity efficiency. Understanding the math behind such randomness reveals both technological nuance and statistical insight — key for professionals shaping next-gen crop environments. **Why This Seed Selection Pattern Matters Now**
In sustainable agriculture circles across the U.S., increasing interest in controlled environment farming — including space-inspired designs — drives demands for intelligent, adaptive systems. Designers configure dispensers to maximize plant variety and resource efficiency, mimicking natural randomness to encourage optimal growth. A 5-activation cycle with only two distinct plant types underscores a deliberate balance: enough diversity to simulate ecological resilience, yet consistency for predictable output. This configuration may appear elementary, but behind it lies statistical precision — shaping everything from yield predictions to system reliability. Recognizing these underpinnings helps users grasp why seemingly random processes are actually carefully calibrated — a key element in advancing space-adjacent agricultural innovation. **Calculating the Probability: Two Varieties, One Appearing Three Times**
Let’s break down the specific scenario: the dispenser makes five independent selections from eight plant varieties, with exactly two different types appearing — and one of them selected exactly three times. First, select the two plant varieties from eight: that’s C(8,2) = 28 combinations. Then, determine which of the two is the one appearing three times — two choices per pair. For each pair, compute the number of distinct arrangements: choosing 3 out of 5 positions for one variety (the other automatically fills the remaining 2 spots) is C(5,3) = 10 permutations. Each full sequence has probability (1/8)^5, since each selection is independent and random. Multiplying: 28 choices × 2 selections × 10 arrangements = 560 favorable outcomes, each with probability (1/8)^5. Total probability: 560 / (8^5) = 560 / 32,768 = 0.01706 — or roughly 1.71%. This precise calculation reveals the rarity of such outcomes in automated seed systems, highlighting both design constraints and randomness basics. **Common Questions About Probability in Automated Seed Systems**
**3.1 How likely is exactly two distinct plants, with one appearing three times?**
The calculated probability confirms it’s relatively rare — about 1.7% chance — due to the strict structure and randomization uniformity.