You need to arrange a list of participants - four administrators and four students - who will sit behind a table in the order listed. In how many ways can you list them if you must alternate students and administrators?
This question is from Discrete Mathematics for Computer Scientists by Stien, Drysdale and Bogart.
Here is what I am thinking they be arrange two ways
In both 1 & 2, you can arrange by (4*3*2*1) students and (4*3*2*1) admins. My solution would be: (4! + 4!) * 2 = 4*4!.
The text does not provide a solution, so I hope someone here can confirm.