In a certain game, a one-inch square piece is placed in the lower-left corner of an eight-by-eight grid made up of

In a certain game, a one-inch square piece is placed in the lower-left corner of an eight-by-eight grid made up of one-inch squares. If the piece can move one grid up or to the right, what is the probability that the center of the piece will be exactly \(4\sqrt2\) inches away from where it started after \(8\) moves?

A. \(\dfrac{24}{256}\)

B. \(\dfrac{64}{256}\)

C. \(\dfrac{70}{256}\)

D. \(\dfrac{128}{256}\)

E. \(\dfrac{176}{256}\)

[spoiler]OA=C[/spoiler]

Source: Princeton Review