A family of 2 parents and 4 children is eating lunch at a rectangular table with 2 chairs on each side and one chair on each end. In how many ways can they be arranged if the two parents sit in the two end chairs?

a. 12
b. 30
c. 36
d. 48
e. 720

There are 6 open seats.

_ _ _ _ _ _

The first and last seat are taken by the two parents.
-For the 1st seat, either parent can sit on the 1st seat -> 2 ways
-Therefore, the last seat, the remaining parent sits on the last seat. -> 1 way

The 4 middle seats are seated by taken by the children.
-For the 1st middle seat, either 4 children can sit on that seat -> 4 ways
-Then for the 2nd middle seat, the remaining 3 children can sit on that seat -> 3 ways
-3rd middle seat -> 2 ways
-4th middle seat -> 1 way

If you multiple the number of ways:
(2 ways)*(1 way)*(4 ways)*(3 ways)*(2 ways)*(1 way) = 48 ways

The answer should be D.