# How many ways can seven people be seated around a circular table such that two of them are always together?

## How many ways can seven people be seated around a circular table such that two of them are always together?

Since in this question we have to arrange persons in a circle and 7 persons have to be arranged in a circle so that every person shall not have the same neighbor. Hence there are 360 ways to do the above arrangement and therefore the correct option is A. So, the correct answer is “Option A”.

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## How many ways can 5 people be seated around a circular table if 2 of the people must be seated next to each other?

As the two person A and B can be arranged as AB or BA, total number of arrangements with the two persons next to each other is 2 x 120 = 240 ways. There are 5 x 4 x 3 x 2 x 1 = 120 ways to seat 5 people in a row.

How many ways can 7 boys and 4 girls can be seated in a round table if the girls are to be seated separately?

7*6*5*4=604,800 arrangements.

### How many ways can a party of 8 people be seated in a circular table if 3 of them insist on sitting side by side?

How many ways 8 persons be seated around a circular table facing the center such that 3 particular persons are always together? entities. So these can be arranged across a circular table in (6−1)! =5!

### How many ways can 7 people be seated at a table?

Seven people can be seated in 6! ⋅2! =1440 ways, if two of them must be seated together.

How many ways can 7 people be seated around a table?

If we are using chairs, then the number of combinations is (7−1)! as previously noted. However if we are using a circular bench, then the location of the first two sitters is irrelevant. Accordingly the next five sitters can be placed in (7−2)! =720 ways.

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#### How many ways can 6 persons be seated around a circular table?

So the number of ways 6 people can be seated around a round table becomes 1x5x4x3x2x1=120.

#### How many ways can 6 people be seated in 6 chairs?

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.

How many ways can 4 boys and 4 girls be seated at a round table if the girls and boys are to occupy alternate seats?

Thus, there are 4! 3! =144 ways of sitting the girls in which the boys and girls alternate seats.

## What is circular permutation?

Circular permutation is the total number of ways in which n distinct objects can be arranged around a fix circle.

## How many ways can 6 persons be seated at a round table?

How many different ways can 8 people be seated around a table?

Number of ways in which 8 people can sit around a table. Sitting around a table is equivalent to circularly arranging the 8 people. Thus, the number of arrangements = (8-1)! = 7!

### How many ways can 6 people sit around a circular table?

Now the remaining seats differ since a new person may sit to the right or left (clockwise/anticlockwise) of the first person, therefore there are 6! ways for 6 people to be situated around the table (with one place already taken by the first person). Therefore there are 1 × 6! ways for people to sit around a circular table.

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### How many ways can seven boys be seated at a table?

Therefore, there are (21*2*120) = 5040 ways that seven boys can be seated at a round table so that any two boys are next to each other. If it is a case of two particular boys instead of any two boys; the answer shall be in (2 * 120) ways = 240 ways.

How do I seat 7 people at a table with chairs?

Seating 7 people at a table where each seat is numbered, and seating 7 people at a table where the chairs are not numbered. When sitting at a table with chairs that are not numbered we will want to begin by placing the first person. At first you may think you have 7 places to seat him!

#### Do you count two seatings around a table as the same?

It’s not unreasonable to count two seatings around the table which only differ by a rotation as “the same”. On the other hand, if the chairs and the view from the chairs are different, it might make more sense to count those seatings as different.