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Home » You Wont Believe How Addictive These Puzzle-Free Games Are—Play Without Blocks! - inBeat

You Wont Believe How Addictive These Puzzle-Free Games Are—Play Without Blocks! - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 5Question: A robotics engineer is programming a robot to assemble components in a specific sequence using 5 different parts: A, B, C, D, and E. If the robot must place these parts in a line such that A comes before B and C comes before D, how many valid sequences can the robot produce?

📌 Solution: We are given 5 distinct parts: A, B, C, D, and E, and we are to count the number of permutations where A appears before B and C appears before D.

📌 First, the total number of permutations of 5 distinct parts is $5! = 120$.

📌 In any random permutation, the relative order of A and B is equally likely to be A before B or B before A. So, exactly half of the permutations have A before B. Similarly, exactly half have C before D.

📌 These two events (A before B and C before D) are independent, because the positions of A and B do not affect the relative order of C and D (since all parts are distinct and no further constraints are linked).

📌 Therefore, the number of permutations satisfying both conditions is:

📌 \frac{1}{2} \times \frac{1}{2} \times 5! = \frac{1}{4} \times 120 = 30

📌 Thus, the robot can produce $\boxed{30}$ valid sequences.

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