A4. A hilltop and a valley are connected by 4 paths. In how many ways can we climb up the hill and then descend, if we can return by the same path?
(A) 4
(B) 8
(C) 12
(D) 16
(E) None of the above.
A4 All options are, according to the basic theorem of combinatorics, $4 \cdot 4=16$.