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Home » Solving for \( x \), we get \( x = 8 \). - jntua results

Solving for \( x \), we get \( x = 8 \). - jntua results

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Within the block, the 3 public health officials can be arranged among themselves in $ 3! = 6 $ ways.

📌 Thus, the total number of arrangements is:

📌 \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:

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\[ 37a + 7b + c = 45 \quad \text{(E3)} \]
Subtract E1 from E2:
\[ (19a + 5b + c) - (7a + 3b + c) = 25 - 11 \]
\[ 12a + 2b = 14 \Rightarrow 6a + b = 7 \quad \text{(E4)} \]
\[ (37a + 7b + c) - (19a + 5b + c) = 45 - 25 \]
\[ 18a + 2b = 20 \Rightarrow 9a + b = 10 \quad \text{(E5)} \]
\[ (9a + b) - (6a + b) = 10 - 7 \Rightarrow 3a = 3 \Rightarrow a = 1 \...
Substitute \( a = 1 \) into E4:
\[ 6(1) + b = 7 \Rightarrow b = 1 \]
Substitute \( a = 1 \), \( b = 1 \) into E1:

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