Task order problem: Task1 must be completed before Task2 and Task3; Tasks 2 and 3 are independent of each other. How many valid total orders exist for the three tasks?

• A. Six
• B. One
• C. Two
• D. Three

Answer: (C)

Counting valid sequences under a precedence constraint. Here, Task1 must come before both Task2 and Task3, while Task2 and Task3 have no order relative to each other. That means Task1 must occupy the first position. After that, Task2 and Task3 can be arranged in either order, since there’s no constraint between them. So the two possible total orders are: Task1, Task2, Task3 and Task1, Task3, Task2. There are exactly two valid total orders.