What Is the Probability of Two Specific People Sitting Next to Each Other?

  • Thread starter Thread starter pivoxa15
  • Start date Start date
Click For Summary
SUMMARY

The probability of two specific people sitting next to each other in a group of six people around a table is definitively calculated as 2/5. The total number of arrangements is represented by 5! due to the circular seating arrangement. When considering the two specific individuals as a single unit, the arrangement simplifies to 4! for the remaining groups, multiplied by 2! for the internal arrangement of the two individuals. This confirms that the correct probability is indeed 2/5, as opposed to the incorrect suggestion of 1/5.

PREREQUISITES
  • Understanding of basic probability concepts
  • Familiarity with factorial notation and calculations
  • Knowledge of circular permutations
  • Ability to analyze combinatorial problems
NEXT STEPS
  • Study circular permutations in combinatorial mathematics
  • Learn about probability theory fundamentals
  • Explore advanced topics in combinatorial probability
  • Practice problems involving arrangements and groupings
USEFUL FOR

This discussion is beneficial for students studying probability, educators teaching combinatorial mathematics, and anyone interested in solving seating arrangement problems.

pivoxa15
Messages
2,250
Reaction score
1

Homework Statement


A group comprising 6 peoiple is sitting around a table. Find the probability that two particular people are sitting next to each other.


Homework Equations





The Attempt at a Solution



4!2!/5!=2/5 because total number of possibities is 5!. If 2 people are to be next to each other than there are 5 groups so 4! choices with each choice, one can swap the group of two. So times by 2!.


BUt the answers suggested 1/5
 
Physics news on Phys.org
Some really dubious 'answers' are being suggested to you. The answer is clearly 2/5. Pick one of the particular people. There are 2 people sitting next to him and 3 not. The odds the other particular person is in the former group is 2/5.
 
Last edited:
That is a nice way of doing it.
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 16 ·
Replies
16
Views
4K
Replies
7
Views
3K
  • · Replies 20 ·
Replies
20
Views
4K
Replies
2
Views
2K
  • · Replies 18 ·
Replies
18
Views
2K
  • · Replies 6 ·
Replies
6
Views
5K
  • · Replies 7 ·
Replies
7
Views
2K