Final answer:
There are 24 different ways for 5 people to be seated in a row with Frankie necessarily sitting in the middle, as the other 4 seats can be filled by the remaining 4 people in 4 factorial (4!) ways.
Step-by-step explanation:
The question asks in how many ways can 5 people sit in a row of 5 seats if Frankie must sit in the middle? To solve this, we consider that Frankie's seat is fixed. With Frankie in the middle seat, there are 4 remaining seats to be filled by the other 4 people.
For the first seat (to Frankie's left), there are 4 choices of people to sit. After selecting someone for that seat, there are 3 remaining people for the next seat, then 2 for the seat after that, and finally, the last person will take the remaining seat.
With this in mind, we can calculate the total number of ways the individuals can be seated using the formula for permutations of n objects taken r at a time, which, in this case, is 4 factorial (4!) because there are 4 seats and 4 people left after Frankie takes the middle seat. Therefore, the number of ways is 4! = 4 x 3 x 2 x 1 = 24.
So, there are 24 different ways the 5 people can be seated with Frankie in the middle seat.