Let 10 red balls and 10 white balls be arranged in a straight line such that 10 each are on either side of a central mark. The number of such symmetrical arrangements about the central mark is\\
(A) $\frac { 10 ! } { 5 ! 5 ! }$\\
(B) $10 !$\\
(C) $\frac { 10 ! } { 5 ! }$\\
(D) $2 \cdot 10 !$