Question

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; the number of such possible arrangements is

Answer 1

for me it should be something like this 6!×18!×2

Answer 2

The total possible permutations of this case would be

6! * 18! * 2!

For the first row, number of teachers is given to be 7.

Separating the Principle, we have 6 teachers and 6 remaining positions,

So, we can have 6! ways of sitting them.

For the second row, total number of students is given to be 20.

Separating the Two tallest students, we have 18 students and 18 remaining positions.

So, we can have then standing in 18! ways

The two tallest students can Interchange their positions, so the ways of their standing would be 2!

The total possible permutations of the case would be

6! * 18! * 2!