Six people attend the theater together and sit in a row with exactly six seats
a. How many ways can they be seated together in the row?
b. 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 be seated together in the row with the doctor in an aisle seat?
c. Suppose the six people consist of three married couples and each couple wants to sit together with the husband on the left. How many ways can the six be seated together in the row?
I will take a look at this:
a - 6 people can be seated, without restrictions, in 6! = 720 ways.
b - If one sits in a fixed seat, the other 5 can be seated in 5! = 120 ways.
c - 3 couples can be seated in: 3 x 3 = 9 ways.