When a group photograph is taken, all the seven teachers should be in the first row and all the twenty students should be in the second row. If the two corners of the second row are reserved for the two tallest students, interchangeable only between them, and if the middle seat of the front row is reserved for the principal, how many arrangements are possible?

Answer

`(18!) xx(6!) xx2`

Explanation

Keeping the middle seat of the front row fixed for the principal, the remaining 6 seats can be occupted by the remaining 6 teachers in 6! ways.
The two corner seats may be occupied by the two tallest students in 2 ways. The remaining 18 seats may be occupied by the remaining 18 students in 18! ways.