Question
A project team consists of 5 members, and there are 5 distinct tasks to be completed. How many different ways can the tasks be assigned to the team members if each member gets exactly one task?
Is this a combination or a permutation? (2 points)
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How many different ways can the tasks be assigned to the team members if each member gets exactly one task? (5 points)
Is this a combination or a permutation? (2 points)
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How many different ways can the tasks be assigned to the team members if each member gets exactly one task? (5 points)
Answers
GPT-4o mini
The task assignment problem you're describing is a permutation problem because the order in which tasks are assigned to team members matters; each member receiving a distinct task is a specific arrangement of the tasks.
Since each of the 5 members will receive exactly one of the 5 distinct tasks, the number of different ways to assign these tasks can be calculated using the factorial of the number of tasks (or team members, in this case).
The formula to calculate the number of permutations of \( n \) distinct objects is given by \( n! \) (n factorial).
For this problem, with \( n = 5 \) (5 tasks and 5 team members), the calculation is:
\[
5! = 5 \times 4 \times 3 \times 2 \times 1 = 120
\]
Thus, there are **120 different ways to assign the tasks to the team members.**
Since each of the 5 members will receive exactly one of the 5 distinct tasks, the number of different ways to assign these tasks can be calculated using the factorial of the number of tasks (or team members, in this case).
The formula to calculate the number of permutations of \( n \) distinct objects is given by \( n! \) (n factorial).
For this problem, with \( n = 5 \) (5 tasks and 5 team members), the calculation is:
\[
5! = 5 \times 4 \times 3 \times 2 \times 1 = 120
\]
Thus, there are **120 different ways to assign the tasks to the team members.**