SOLUTION: a)How many ways can 10 questions on a test be arranged? b)How many ways can 10 questions be arranged on a test, if the easiest and the most difficult questions are side by side?

(a)  10! = 10*9*8*7*6*5*4*3*2*1 = 3628800 ways.


     Any of 10 questions can be placed first;

     any of remaining 9 questions can be placed 2-nd;

     any of remaining 8 questions can be placed 3-rd

         . . . . and so on . . . . 



(b)  We can consider two special questions as one single object in 2 states, that are its internal permutations AB and BA.


    Then we have 9 objects and 9! their permutations with one the special object which has 2 states.


    Therefore, in all, there are  2*9! different ways = 725760 ways.



(c)  From the entire set of all possible permutations of 10 questions, subtract the number of (b) to get the answer


     10! - 2*9! = 725760 = 3628800 - 725760 = 2903040.