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Home » This Myth of a Shiny Gimmighoul Is Too Irresistible to Ignore! - Databee Business Systems

This Myth of a Shiny Gimmighoul Is Too Irresistible to Ignore! - Databee Business Systems

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \times 6 = 720

📌 \boxed{720}

📌 Question: A palynologist has 5 red pollen grains, 3 green pollen grains, and 2 blue pollen grains. If she randomly selects 6 grains from the bag without replacement, what is the probability that exactly 2 red, 2 green, and 2 blue grains are selected?

📌 We begin by computing the total number of ways to choose 6 grains from the total of $ 5 + 3 + 2 = 10 $ grains:

📌 \binom{10}{6} = 210

📌 Next, we compute the number of favorable outcomes: selecting exactly 2 red, 2 green, and 2 blue grains. Since there are 5 red grains, 3 green, and 2 blue, the number of favorable combinations is:

📌 \binom{5}{2} \times \binom{3}{2} \times \binom{2}{2} = 10 \times 3 \times 1 = 30

📌 \frac{30}{210} = \frac{1}{7}

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