Permutation(排列) 1題

Step 1 : Put the dictionary in the upper or lower shelf [C(2,1)].
Step 2 : Put the comic in another shelf [C(1,1)].
Step 3 : Select 3 fictions to the lower shelf [C(5,3)] and 2 to the upper shelf[C(2,2)].
Step 4 : Arrange the 4 books on the lower shelf [P(4,4)] and the 3 on the upper[C(3,2)].

The number of arrangement of the books
= C(2,1) x C(1,1) x C(5,3) x C(2,2) x P(4,4) x P(3,3)
= (2!/1!1!) x (1!/1!0!) x (5!/3!2!) x (2!/2!0!) x 4! x 3!
= 2 x 1 x 10 x 1 x 24 x 6
= 2880