Agroup 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:

       3         *         1               *     2               *      2         *         1           = 12

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

In this case:

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

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

       3         *         2               *     2               *      1         *         1           = 12

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

       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

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step-by-step explanation:

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