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Home » \textAverage Speed = \frac{\textTotal Distance}{\textTotal Time} = \frac4207 = 60 \text km/h - Blask

\textAverage Speed = \frac{\textTotal Distance}{\textTotal Time} = \frac4207 = 60 \text km/h - Blask

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 $ k = 2 $: $ (-1)^2 inom{4}{2} \cdot 2^6 = 1 \cdot 6 \cdot 64 = 384 $

📌 $ k = 3 $: $ (-1)^3 inom{4}{3} \cdot 1^6 = -1 \cdot 4 \cdot 1 = -4 $

📌 $ k = 4 $: $ (-1)^4 inom{4}{4} \cdot 0^6 = 1 \cdot 1 \cdot 0 = 0 $

📌 - 2916 + 384 - 4 + 0 = 1560

📌 Thus, there are 1560 distinct 6-day sequences where each experiment type is used at least once.

📌 oxed{1560}

📌 Question: A computer scientist uses a randomization algorithm that generates a 5-character code using the letters A, B, C, D, and E, each used at most once, with the middle character fixed as B. How many valid codes can be generated under this rule?

📌 Solution: The code has 5 positions: _ _ _ _ _. The middle (3rd) character is fixed as B. We must choose 4 distinct letters from {A, B, C, D, E}, with B fixed in position 3, so the remaining 4 positions use the other 4 letters, but B is already placed, so we use A, C, D, E for the other 4 positions.

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