How many ways can 7 boys be seated at a round table so that 2 particular boys are next to each other?

The number of ways in which 7 boys sit in a round table so that two particular boys may sit together is. 240.

How many ways can 7 boys and 4 girls can be seated in a round table if the girls are to be a seated separately 3 marks b seated together 3 marks?

7*6*5*4=604,800 arrangements. It’s also 7! / 3! Let us seat the boys first.

How many ways are there for 7 people to sit in a row if two people have to sit at least two seats apart?

That can be done in 2⋅6! =1440 ways.

How many ways can 7 students be seated at a round table?

Originally Answered: In how many ways can 7 people be seated around a circular table if 2 people must not seat together? Suppose the 2 people are together – you are to arrange 6 ‘units’ around the table. This can be done in [6 – 1]! = 120 ways.

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 at round 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.

How many ways can you seat 7 boys in a table?

There’s just one way to seat 2 boys, two ways to add a third. The number of ways to add a next boy is equal to the number of gaps between the boys already seated, which since we have a round table is equal to the number of boys already seated. So to accommodate 7 boys there are 1*2*3…*6 = 6! or 720 ways.

How many people can sit around a circular table?

Hence the number of arrangements (or ways) in which four different persons can sit around a circular table = (4 – 1)! = 3! = 6. Ques. In how many ways can 5 boys and 5 girls be seated at a round table so that no two girls may be together?

How many ways can a group of two boys be arranged?

Now, a group of two boys can be chosen in (7C2) = 21 ways. Now, each such ‘two-boy group’ can be arranged in 2 ways (say, ‘AE’ and ‘EA’). Now, when these two boys will sit next to one another, they are to be treated as a single entity. So, virtually, it becomes a permutation of (7 -2 + 1) = 6 characters around a round table.

How many different ways can you seat the same person?

If you choose 2 men and 3 women or 3 men and 2 women, there are 6*1+4*3 = 18 ways to do it. You can seat the first of whichever sex has two sitters in 5 ways, the second one in 4, divide by two because you could switch the order you selected them, so that’s 10 arrangements. 18*10 = 180.