Linked Questions

9
votes
3answers
14k views

Probability question about married couples

If four married couples are arranged in a row, what is the probability that no husband sits next to his wife? Would it be $1- \frac{2(4!)}{8!}$?
1
vote
4answers
2k views

Arranging Couples in a Row

Three couples are sitting in a row. Compute the number of arrangements in which no person is sitting next to his or her partner. Answer is 240. From wikipedia, This problem is called the menage ...
0
votes
3answers
8k views

No husband can sit next to his wife in this probability question

I have a probability question that reads: Question: If 4 married couples are arranged in a row, find the probability that no husband sits next to his wife. My attempt: ...
5
votes
1answer
6k views

Classic $2n$ people around a table problem

A total of $2n$ people, consisting of $n$ married couples, are randomly seated (all possible orderings being equally likely) at a round table. Let $C_i$ denote the event that the members of couple $i$ ...
3
votes
2answers
4k views

Probability of Couples sitting next to each other (Sitting in a Row)

Suppose we have 4 couples and 8 seats. The seats are oriented such that it is a row. The people take their seats in a random fashion. What is the probability that 2 couples sit next to each other? ...
7
votes
1answer
6k views

Deriving the 37-percent rule for dating

I am trying to prove the theoretical "37-percent rule" for dating. The setup, if I remember correctly, is this. Suppose that you will meet exactly $N$ potential mates in your life, and you will meet ...
0
votes
1answer
2k views

Four married couples, eight seats. Probability that husband sits next to his wife?

There are four married couples and eight seats. When they sit, what is the probability that husband sits adjacent to his wife? The answer to this problem is 12/35 I can arrive at this answer when I ...
10
votes
1answer
2k views

In how many ways can n couples (husband and wife) be arranged on a bench so no wife would sit next to her husband?

In how many ways can n couples (husband and wife) be arranged on a bench so no wife would sit next to her husband? I thought about this: (Total amount of ways to sit 2n people in 2n sits)-(Using ...
4
votes
2answers
657 views

Probability that no couple sits together in a circle

Suppose $n$ couples are seated in a circle, and let $P_n$ be the probability that no couple is sitting together. Using Inclusion-Exclusion, I believe it can be shown that $\hspace{.2 in}\...
4
votes
2answers
277 views

List of non-immediately-repeating permutations

Background: I am trying to design a scientific trial (computer science dissertation) in which participants will answer 8 questions. There are in fact only 4 questions but each is asked in two ...
2
votes
2answers
80 views

Number of possible routes through n countries and 2n cities, with restrictions

Someone is planning a round-the-world trip that involves visiting $2n$ cities, with two cities from each of $n$ different countries. He can choose a city to start and end the journey in, with ...
0
votes
0answers
49 views

A question regarding Poisson approximation

Before I pose my question I just want to note that I know that this question here been asked here before but the responses were only partially helpful. A total of $2n$ people, consisting of $n$ ...
0
votes
0answers
35 views

How many string of numbers $1,…,n$ of length $2n$ where two of the same numbers are not consecutive. [duplicate]

I need to find the number of strings of length $2n$ that consist of numbers $1,...,n$ each appearing exactly twice and not next to each other. Let $f(n)$ denote the function that gives me back that ...