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

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In summary, the probability of two particular people sitting next to each other in a group of 6 people sitting around a table is 2/5. This is based on the fact that there are 5 groups of 4! choices and each choice can be swapped with a group of 2, resulting in a total of 2! combinations.
  • #1
pivoxa15
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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
 
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  • #2
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:
  • #3
That is a nice way of doing it.
 

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

What is a 4th Combinatorial Problem?

A 4th Combinatorial Problem is a type of mathematical problem that involves finding all possible combinations of a set of elements, often with certain constraints or restrictions. It is a subfield of combinatorics, which is a branch of mathematics concerned with counting and arranging objects.

What are the applications of 4th Combinatorial Problems?

4th Combinatorial Problems have a wide range of applications in various fields such as computer science, statistics, economics, and genetics. They are used to solve problems related to scheduling, optimization, enumeration, and decision making.

How do you approach solving a 4th Combinatorial Problem?

The approach to solving a 4th Combinatorial Problem depends on the specific problem at hand. Generally, it involves identifying the elements in the problem, determining the constraints and restrictions, and then using techniques such as permutation, combination, or graph theory to find all possible combinations.

What are some common techniques used in solving 4th Combinatorial Problems?

Some common techniques used in solving 4th Combinatorial Problems include brute force enumeration, dynamic programming, backtracking, and greedy algorithms. These techniques help to efficiently generate and evaluate all possible combinations to find the optimal solution.

How do 4th Combinatorial Problems differ from other types of combinatorial problems?

4th Combinatorial Problems are distinguished from other types of combinatorial problems by the number of elements involved in the problem. 4th Combinatorial Problems typically involve finding combinations of four elements, while other types may involve more or fewer elements. Additionally, 4th Combinatorial Problems often have specific constraints or restrictions that must be considered in the solution process.

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