Eight people are to be seated in a row of 8 chairs. In how many ways can these people be seated if two of them insist on sitting next to one another?

Solution:

Given there are 8 people and 8 chairs in a row

Since two people insist on sitting next to each other, they are considered as one unit

So now, we have 7 chairs and 7 people

We can arrange them in 7! ways

But we know that the two people(taken as one unit) can interchange their places , i.e. in 2 ways

Therefore, there are 7! *2 = 5040 *2 = 10080 ways

Eight people are to be seated in a row of 8 chairs. In how many ways can these people be seated if two of them insist on sitting next to one another?

Summary:

Eight people are to be seated in a row of 8 chairs. In 10080 ways can these people be seated if two of them insist on sitting next to one another.