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 5!5!.

5!=5×4×3×2×1=1205! = 5 \times 4 \times 3 \times 2 \times 1 = 120

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:

  1. How many ways can 6 people sit in 6 seats?
  2. What if 3 seats were available for 5 people? How many ways could this be done?
  3. How many ways can 5 people sit in a circle instead of in a row?
  4. What if some of the 5 people were indistinguishable? How would that affect the number of ways?
  5. 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