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Home » The Most Iconic Pokémon Protagonists That Defined Generations of Gamers! - Treasure Valley Movers

The Most Iconic Pokémon Protagonists That Defined Generations of Gamers! - Treasure Valley Movers

📅 April 18, 2026 👤 scraface

Apr 18, 2026

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📌 P(\text{at least one of each color}) = \frac{630}{1365}

📌 \frac{630}{1365} = \frac{6}{13}

📌 \boxed{\frac{6}{13}}

📌 Question: A transportation analyst is analyzing a network with 6 red buses, 4 green buses, and 5 blue buses. If she randomly selects 5 buses for maintenance, what is the probability that she selects at least two buses of each color?

📌 We are selecting 5 buses from a total of $ 6 + 4 + 5 = 15 $ buses.

📌 We want the probability that the selection includes **at least two buses of each color**.

📌 ### Step 1: Total number of ways to choose 5 buses from 15:

📌 \text{Total ways} = \binom{15}{5} = 3003

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Multiply both sides by \(u\) (assuming \(u
u^2 + 1 = 3u \quad \Rightarrow \quad u^2 - 3u + 1 = 0.
u = rac{3 \pm \sqrt{9 - 4}}{2} = rac{3 \pm \sqrt{5}}{2}.
So \( u = rac{3 + \sqrt{5}}{2} \) or \( u = rac{3 - \sqrt{5}}{2} \).
Now recall \( u = rac{x+y}{x-y} \). Let \( r = rac{x}{y} \), assumin...
e 0\). Then:
rac{x+y}{x-y} = rac{r+1}{r-1}.
Set this equal to each value of \(u\):
Case 1:** \( rac{r+1}{r-1} = rac{3 + \sqrt{5}}{2} \)
2(r+1) = (3 + \sqrt{5})(r - 1)

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