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Home » Roger Ebert Uncovered: The Shocking Truth Behind His Most Controversial Critique! - AMAZONAWS

Roger Ebert Uncovered: The Shocking Truth Behind His Most Controversial Critique! - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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

📌 ### Step 2: Favorable outcomes — at least two of each color

📌 We are looking for selections with **at least 2 red, 2 green, and 2 blue** buses. But since we're only selecting 5 buses, it's **impossible** to have at least 2 of each color (since $2+2+2 = 6 > 5$).

📌 Thus, the number of favorable outcomes is:

📌 ### Step 3: Compute the probability

📌 P(\text{at least 2 of each color}) = \frac{0}{3003} = 0

📌 Question: A historian of science is organizing a panel with 3 experts selected from a list of 6 historians, 5 scientists, and 4 physicians. What is the probability that the panel includes at least one expert from each profession?

📌 We are selecting 3 experts from a total of $ 6 + 5 + 4 = 15 $ professionals.

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Multiplying through by \(k(k+1)\) gives:
= A(k+1) + Bk = Ak + A + Bk
= (A + B)k + A
For the equation to hold for all \(k\), we set up the system:
A + B = 0 \quad \text{and} \quad A = 1
Solving this, we find \(A = 1\) and \(B = -1\). Thus:
Now, substitute this into the sum:
This is a telescoping series, where most terms cancel out:
After cancellation, we are left with:
Thus, the sum is:

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