How many ways can 5 friends be seated around a circular table?

How many ways can 5 friends be seated around a circular table?

24
In how many different ways can five people be seated at a circular table? So the answer is 24.

How many ways can six people be seated at a circular table if one of them is to be seated at a certain chair?

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. (i) A and B always sit together. (ii) C and D never sit together.

How many ways can eight knights of the round table be seated if one of them must sit to the right of King Arthur?

There are 8 such “identical rotations” for each possible seating arrangement so the total number of seatings is 8! / 8 = 7! = 5040.

How many ways can 10 different chairs be arranged in a circle?

But there are 10 possible such points. So there are 10 ways of seating 10 people abreast for every way of seating them at a round table. It follows that the number of ways of seating 10 people at a round table = 10!/10 = 9! = 362,880.

How many can 5 persons be seated in a row of 7 chairs?

5! ⋅2! =21 ways of choosing which 5 chairs from the 7 will have people sitting in them.

How many different ways can 5 students be seated in a row?

So, 5 people can be seated in 5 seats in 120 ways.

How many ways can a party of 7 persons arrange themselves around a circular table?

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

How many ways can 6 people sit around the circular table?

Originally Answered: How many ways can 6 people sit at a circular table? Infinitely many ways. Unless you’re implying 6 discrete spots, in which case it is 6! = 720 ways.

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

Complete step-by-step answer: 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.

How many ways can 5 people be seated around a circular table if two of them insist on sitting beside 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 5 persons be seated in a row inside the Theatre?

So there are 120 different ways to seat 5 girls in 5 chairs.

How many ways can 10 students be seated in a row of 10 chairs?

= 3265920 ways for the ten people to be seated so that a certain to are not next to each other.

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.

How many ways can two people sit next to each other?

2. at a round table there is (n-1)!. If it would not matter if the 2 particular people sat next to each other then the answer would be (7-1)! or 6! or 720. But from those 6! or 720 ways, we must subtract the number of ways those two particular persons can sit next to each other.

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!

How many possible rotations are there for 7 chairs?

But when they are joined in a circle, a rotation still counts the same way of seating everyone. You’ll notice that there are 7 possible rotations in this case (since seven chairs). So we partition the result from the straight line into 7 groups.