Match the pairs in the following questions by writing the corresponding letters only.
$\begin{array}{|cl|cl|} \hline A. & \text{The number of distinct binary tree with n nodes.} & P. & \frac{n!}{2} \\ \hline B. & \text{The number of binary strings of the length of 2n} & Q. & \binom{3n}{n} \text{ with an equal number of 0’s and 1’s} \\ \hline C. & \text{The number of even permutation of n objects.} & R. & \binom{2n}{n} \\ \hline D. & \text {The number of binary strings of length 6n which are} & S. & \frac{1}{1+n}\binom{2n}{n} \text{ palindromes with 2n 0’s.} \\ \hline \end{array}$