Probability Involving Combinations of Classroom Seating

Click For Summary
SUMMARY

This discussion focuses on calculating probabilities related to classroom seating arrangements for 28 students. The key probabilities discussed are the likelihood of exactly one student being reseated in their original seat and the probability of at least one student returning to their original seat. The approach involves determining the total number of ways to scramble the seating and applying combinatorial principles to find the required probabilities. Specifically, the probability of at least one student reseated in their original position is derived from the complement of the probability that no students are reseated.

PREREQUISITES
  • Understanding of basic probability theory
  • Familiarity with combinatorial mathematics
  • Knowledge of factorial notation and permutations
  • Ability to apply the principle of inclusion-exclusion
NEXT STEPS
  • Study the concept of derangements in combinatorial mathematics
  • Learn how to calculate permutations and combinations
  • Explore the principle of inclusion-exclusion for probability calculations
  • Investigate advanced probability topics such as random variables and expected values
USEFUL FOR

This discussion is beneficial for students, educators, and mathematicians interested in probability theory, particularly those exploring combinatorial problems and their applications in real-world scenarios.

v_bledsoe
Messages
1
Reaction score
0
I am attempting to determine two probabilities in a scenario in which a classroom of 28 students with assigned seating is scrambled randomly and blindly reseated by the teacher. What is the probability that exactly one student is reseated in his or her original seat, and what is the probability that at least one student is reseated in his or her original seat. Thanks for the assistance!
 
Physics news on Phys.org
First of all, how many ways are there to scramble 28 things?

How many ways are there to fix 1 and scramble the other 27?

The probability that at least one student is reseated in his or her original seat is one minus the probability that no student is reseated in his or her original seat.
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
3K
Replies
29
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
4K
Replies
7
Views
7K
  • · Replies 2 ·
Replies
2
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
8K
  • · Replies 18 ·
Replies
18
Views
3K