SOLUTION: mr. santos has set 8 questions for a math test. c.) if the most difficult question and the easiest one are set next to each other, how many permutations are there for the 8 ques

8 items have 8! = 8*7*6*5*4*3*2*1 = 40320  permutations.


But in this problem, we consider not all the permutations.


We consider only THOSE, where the most difficult question and easiest question are set next to each other.


So, these two questions always are neighbor.


It means, that we consider these two objects as two clued together;

so we actually consider 7 objects, and this special object can exist in two states (ED) or (DE), depending

which one of the two questions, easy (E) or difficult (D), goes first.



THEREFORE, the total number of all such possible permutations is 


    2*7! = 2 * (7*6*5*4*3*2*1) = 2 * 5040 = 10080.    ANSWER