A box contains 10 red cards numbered $1, \ldots, 10$ and 10 black cards numbered $1, \ldots, 10$. In how many ways can we choose 10 out of the 20 cards so that there are exactly 3 matches, where a match means a red card and a black card with the same number?\\
(A) $\binom { 10 } { 3 } \binom { 7 } { 4 } 2 ^ { 4 }$\\
(B) $\binom { 10 } { 3 } \binom { 7 } { 4 }$\\
(C) $\binom { 10 } { 3 } 2 ^ { 7 }$\\
(D) $\binom { 10 } { 3 } \binom { 14 } { 4 }$