How many ways can 7 students be seated in a row of 7 seats if two of the students insist on sitting beside each other?

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

What is the probability of two people sitting next to each other?

Answer To The Probability Of Sitting Next To Someone Of which, there are 2 spots adjacent to a–one to the left and one to the right (shown in green in the following diagram). Therefore, the probability a and b will be seated next to each other is 2/4 = 1/2.

How many different ways can seven students line up in a row?

5040
7! =7⋅6⋅5⋅4⋅3⋅2⋅1=5040. This particular problem is a permutation.

How many ways can you arrange 7 books?

5040 way. (n+r-1)!/(r!*(

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 different ways students can sit next to each other?

Take the seat numbers as 1,2,3,4,5,6. So the 2 students that insist on sitting next to each other can sit at 1,2 or 2,3, or 3,4 or 4,5, or 5,6 (5 possibilities). So there are 5 * 4! = 5 * 24 = 120 ways that the 6 students can be seated.

Can boys and girls sit together?

Yes, guys, and girls can sit together.

How many ways can the boys and girls sit in row?

According to the solution file provided by Toby Mak, they meant to ask in how many ways the boys and girls can sit in a row, with all girls sitting together and all boys sitting together. In this case we can have B B B G G G or G G G B B B, which again results in 2 ⋅ 3! ⋅ 3! = 72 possible arrangements.

How do you arrange 7 boys in a 7-seater?

First, seat have the 7 boys sit down in a row of 7 seats. There are 7! = 5040 such arrangements. Next, put a seat between each boy, and to either side of the boys on either end of the row – there should be 8 such empty seats. Choose 5 of the 8 seats for the girls to sit in: ( 8 5) = 56. Then arrange the 5 girls in the 5 seats.

How many ways can the boys and girls be arranged?

There can be only one arrangement in which boys and girls can sit. but position of individual boy and girls can be changed. So, there are 5 girls and 5 slots for them that means they can be arranged in 5! ways, similarly boys have 4 slots, so they can be arranged in 4! ways.

How many boys are needed to make up 6 groups?

We know groups 2 through 5 HAVE to have at least 1 boy in each of them, so no 2 girls are together. Therefore, we take 4 boys and place 1 of them in each of those 4 groups. That leaves us with 3 boys to place into the 6 groups. The number of ways of doing that is:

https://www.youtube.com/watch?v=82-uPFpFmMQ