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Home » The Ultimate Marvel Eternity Guide: Inside the Mind-Blowing Truth Behind It All!%, - 500apps

The Ultimate Marvel Eternity Guide: Inside the Mind-Blowing Truth Behind It All!%, - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 inom{6}{3} = rac{6 \cdot 5 \cdot 4}{3 \cdot 2 \cdot 1} = 20

📌 inom{10}{5} = rac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 252

📌 Favorable outcomes: $6 \cdot 20 = 120$.

📌 Probability: $rac{120}{252} = rac{10}{21}$.

📌 Thus, the probability is $oxed{\dfrac{10}{21}}$.

📌 Question: A museum has 7 digital kiosks arranged in a circle for interactive displays. In how many distinct ways can 4 curator-led sessions (each hosted by a different kiosk) be assigned to 4 kiosks, if rotations of the arrangement are considered identical?

📌 Solution: Since the kiosks are arranged in a circle and rotations are considered the same, we fix one session to eliminate rotational symmetry. First, assign 4 out of 7 kiosks to the sessions: $inom{7}{4} \cdot 4!$ would count linear arrangements. But due to circular symmetry, we divide by 4 (the number of rotations).

📌 Alternatively, fix one session at a position to break rotational symmetry. Then choose 3 remaining kiosks from the remaining 6 and assign the other 3 sessions:

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This is a quadratic in \( w \). Factoring:
Since \( w = z^2 \), we have:
z^2 = -2 \Rightarrow z = \pm \sqrt{-2} = \pm i\sqrt{2}
So the solutions are \( z = i\sqrt{2} \) and \( z = -i\sqrt{2} \). Eac...
But wait — \( z^2 = -2 \) has exactly two solutions in \( \mathbb{C} \...
z = \sqrt{2}i, \quad z = -\sqrt{2}i
These are distinct and purely imaginary. The real part of each is 0.
Thus, the sum of the real parts is:
+ 0 = 0
Even though there are four roots? Let's double-check factorization.

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\[ 100a + 10b = 20 \]
\[ 10a + b = 2 \quad \text{(Equation 1)} \]
From condition 3:
\[ 400a + 20b + 2 = 50 \]
\[ 400a + 20b = 48 \]
\[ 20a + b = 2.4 \quad \text{(Equation 2)} \]
Subtract Equation 1 from Equation 2:
\[ (20a + b) - (10a + b) = 2.4 - 2 \]
\[ 10a = 0.4 \]
\[ a = 0.04 \]

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