How many ways can 6 ladies be seated in a circular table such that two of the ladies must always sit beside each other?

Example 1 In how many ways can 6 people be seated at a round table? Solution As discussed in the lesson, the number of ways will be (6 – 1)!, or 120.

How many ways can you arrange 6 people in 6 seats such that none of them are occupying their original positions?

Answer and Explanation: There are 720 ways to seat 6 people in a row. Each seating of 6 people is simply a different ordering of the 6 people in the group. Therefore, the…

How many ways can 5 couples be seated in a circular table if the wives must sit together?

There are 5 such couples, so there are 2^5=32 ways to arrange the couples, for each of those 24 ways to seat the couples.

How many ways can 6 persons be seated in a row?

720
Hence, total number of ways in which six persons can be seated in a row = 6×5×4×3×2×1=720.

How many ways can six people be seated in six seats if the first seat is always occupied by the same person?

720 ways
Therefore, 720 ways are there for six people to sit in a six-passenger car.

How many ways can 6 person be seated in a row?

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

= 120. In this case it would be the same as ordering people on a line. However if rotation symmetry is taken into account, there are five ways for people to sit at the table which are just rotations of each other. So using symmetry the answer is 24.

How many ways can 4 married couples seat themselves around a circular table if spouses sit opposite each other?

Below are two specific examples. Ex2. Mom and dad and their 6 children (3 boys and 3 girls) are to be seated at a table. How many ways can this be done if mom and dad sit together and the males and females alternate?

How many ways can you arrange the couples around the table?

If one couple sits together, the couple can be selected in ( 4 1) ways. 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.

How many people can be seated around a 8-person table?

The following solution uses the Principle of Inclusion and Exclusion (PIE). If we disregard the constraint on couples sitting together, the 8 people can be seated around the table in N = 7! ways. Let’s say an arrangement of the couples has “Property i ” if couple i are seated together, for i = 1, 2, 3, 4.

How many people can sit round a circular table in 120 ways?

Keeping one person fixed, the remaining 5 persons can be seated in (5*4*3*2*1= 5!) 120 ways. So, 6 people can sit round a circular table in 120 ways.

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!