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Home » Let width = \( w \). Then length = \( 2w + 4 \). - go-checkin.com

Let width = \( w \). Then length = \( 2w + 4 \). - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 $ 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.

📌 We fix B in position 3. The remaining 4 positions (1st, 2nd, 4th, 5th) must be filled with the 4 other letters (A, C, D, E), each exactly once â so it's a permutation of 4 distinct letters.

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