How many ways are there to seat n couples around a circular table such that no couple sit next to each other?

There are 720 different permutations of couples.

How many ways can 4 couples be seated in a bench with 8 seats such that each person sits next to their partner?

Therefore, there are 40320 ways that the people can be seated when there is no restriction on the seating arrangement. The possible ways = 7! × 2! Therefore, if persons A and B must sit next to each other there are 10080 ways of seating arrangement.

How many ways can 7 people be arranged into 7 chairs?

5040 ways
So there are 5040 ways of arranging seven people in a row of seven chairs.

What is the m problem?

The m enage problem asks for the number of ways of seating n couples at a circular table, with men and women alternating, so that no one sits next to his or her partner.

What are the number of ways of making 5 couples stand in a line?

Five people can line up in 5! = 120 ways.

What are the no of ways of seating 7 candidates?

3c3 is the answer. 105.

How many ways can 5 couples be seated in a table?

Since the 2nd person must be the spouse of the 1st, there is only one choice (= 1 way). Treating each couple as 1 unit, then the 5 couples can be seated 5! = 120 ways.

What is the number of seating arrangements (permutations) of a round table?

The first couple has a choice of 10 ways to choose 2 seats adjacent to each other at a round table. The remaining 4 couples are then confined to 4! ways to select 4 pairs of seats. Each couple may then arrange to be seated in 2 ways beside one another. The number of seating arrangements (permutations) is therefore = (10) (4!) (2)^5 = 7680.

How many ways of sitting are there in a room?

First couple can sit in 1way directly. Second couple has only 1 way of sitting. As sitting left to couple 1 is same as sitting right to them. Third in 2 ways, fourth in 3, fifth in 4 and finally sixth in 5 ways. Therefore total ways of sitting = 5!

How many objects can be arranged around the table?

The members of the couple can be arranged in 2 ways: man on the left or man on the right. If we consider the couple as one object and all the other people as one object each, then we have 7 objects to arrange around the table, which can be done in 6! ways. So S 1 = ( 4 1) ⋅ 2 ⋅ 6!