Ten couples founded a dance group and decided to establish a board of directors with three positions: president, secretary, and treasurer. For greater representation, it was decided that at most one person per couple could hold a position on this board.
How many different boards can be formed by these 10 couples?\\
(A) $10 \times 9 \times 8$\\
(B) $20 \times 18 \times 16$\\
(C) $20 \times 19 \times 18$\\
(D) $10 \times 9 \times 8 \times 2$\\
(E) $20 \times 18 \times 16 \times 2$