Math Problem Statement
In an experiment on social interaction,
5
people will sit in
5
seats in a row. In how many ways can this be done?
Question content area bottom
Part 1
There are
enter your response here
ways.
Solution
To determine how many ways 5 people can sit in 5 seats, we use the concept of permutations. Since each person is distinct and has a unique seat, the total number of ways to arrange 5 people in 5 seats is given by the factorial of 5, written as .
Thus, there are 120 ways to arrange 5 people in 5 seats.
Would you like further details or have any questions?
Here are 5 related questions you might find interesting:
- How many ways can 6 people sit in 6 seats?
- What if 3 seats were available for 5 people? How many ways could this be done?
- How many ways can 5 people sit in a circle instead of in a row?
- What if some of the 5 people were indistinguishable? How would that affect the number of ways?
- How can the number of ways change if some seats were reserved for specific individuals?
Tip: When dealing with seating arrangements, always think of permutations when the order of people matters.
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Math Problem Analysis
Mathematical Concepts
Permutations
Factorials
Formulas
n! (Factorial of n) where n is the number of distinct items to arrange
Theorems
Permutation theorem
Suitable Grade Level
Grades 6-8
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