A group of 5 friends-Archie, Betty, Jerry, Moose, and Veronica-arrived at the movie theater to see a movie. Because they arrived late, their only seating option consists of 3 middle seats in the front row, an aisle seat in the front row, and an adjoining seat in the third row. If Archie, Jerry, or Moose must sit in the aisle seat while Betty and Veronica refuse to sit next to each Other, how many possible seating arrangements are there?

there are 48 possible seating arrangements.

Step-by-step explanation:

This can be calculated using the rule of multiplication, in which the number of options depends on the following cases:

Betty is sitting on the 1st middle seat:

3 * 1 * 2 * 2 * 1 = 12

Aisle Seat 1st Middle Seat 2nd Middle 3rd Middle 3rd Row Seat

In this case:

There are 3 options for aisle seat: Archie, Jerry or Moose. There is 2 option for 1st middle Seat: Betty. There are just 2 options for the 2nd Middle seat because Veronica can be beside Betty. There are 2 options for 3rd seat: The two friends that we doesn't assign a seat yet. There is 1 option for 3rd row seat.

At the same way, we can calculate the possible seating arrangements in the following cases:

Betty is sitting on the 2nd middle seat:

3 * 2 * 1 * 1 * 1 = 6 Aisle Seat 1st Middle Seat 2nd Middle 3rd Middle 3rd Row Seat

Betty is sitting on the 3rd middle seat:

3 * 2 * 2 * 1 * 1 = 12

Aisle Seat 1st Middle Seat 2nd Middle 3rd Middle 3rd Row Seat

Betty is sitting on the adjoining seat in the third row:

1 * 3 * 3 * 2 * 1 = 18

3rd Row Seat Aisle Seat 1st Middle Seat 2nd Middle 3rd Middle

So, there are 48 possible seating arrangements and it is calculate as:

12 + 6 + 12 + 18 = 48