SOLUTION: Calculate the total number of different permutations of all letters A, B, C, D, E, F when a) there are no restrictions, b) the letters A and B are to be adjacent to one another,

(a)  6! = 6*5*4*3*2*1 = 720.



(b)  You concider the pair of letters AB as one glued object;

     so you have  5 object to permutate, in all, which produces 5! = 5*4*3*2*1 = 120 different permutations.


     Another 120 different permutations you have with the object BA instead of AB.


     So, in total, there are  120 + 120 = 240 such permutations.



(c)  You have 3 possibility for the first letter (A, B or C).

     Similarly, you have 3 possibility for the last letter (D, E or F).

     Finally, you have 4! = 4*3*2*1 = 24 permutations for the remaining 6-2 = 4 letters.


     Hence, in all, there are  3*3*24 = 216  possible permutations, satisfying the imposed conditions.