Linked Questions

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 $1- \frac{2(4!)}{8!}$?
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 ...
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: ...
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 $i$ ...
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? ...
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 ...
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 ...
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 ...
2answers
657 views