Six people attend the theater together and sit in a row with

Six people attend the theater together and sit in a row with exactly six seats between two aisles. Suppose one of the six is a doctor who must sit on the aisle in case she is paged. How many ways can the people seated together in the row with the doctor in an aisle seat?

Solution

The number of ways 5 people can be seated as the doctor sit on aisle = 5! = 120ways

Since there are 2 aisle, the doctor can choose between these two aisle seats = 2 ways

number of ways the people can be seated together in the row with the doctor in an aisle seat = 120 x 2 = 240ways.