Question 786898
Use slot method：
a) 4 and 5 can be placed in different slots. There are 6 outcomes:
_4_ _X_ _5_  _A_ _B_, _X_ _4_ _A_ _5_ _B_, _X_ _A_ _4_ _B_ _5_
_5_ _X_ _4_  _A_ _B_, _X_ _5_ _A_ _4_ _B_, _X_ _A_ _5_ _B_ _4_
(X,A,B are chosen from 1,2,3)
For the first outcome, # of permutations = 1*3*1*2*1=6. The other five have the same number. So the total number of permutations are 6*6 =36.
Your answer is correct but I don't think you made correct explanations.

b)follow the same step as part a),
_4_ _X_ _A_ _5_ _B_, _X_ _4_ _A_ _B_ _5_
_5_ _X_ _A_ _4_ _B_, _X_ _5_ _A_ _B_ _4_
total # of permutations = 4* (1* 3*2*1*1）= 24

c) _4_ _X_ _A _ _B_ _5_, _5_ _X_ _A _ _B_ _4_
total # of permutations = 2*(1*3*2*1*1)= 12