Let \(\left(\begin{array}{l}n \\ k\end{array}\right)\) denotes \({ }^{n} C_{k}\) and \(\left[\begin{array}{l} n \\ k \end{array}\right]=\left\{\begin{array}{cc}\left(\begin{array}{c} n \\ k \end{array}\right), & \text { if } 0 \leq k \leq n \\ 0, & \text { otherwise }\end{array}\right.\) If \(A_{k}=\sum_{i=0}^{9}\left(\begin{array}{l}9 \\ i\end{array}\right)\left[\begin{array}{c}12 \\ 12-k+i\end{array}\right]+\sum_{i=0}^{8}\left(\begin{array}{c}8 \\ i\end{array}\right)\left[\begin{array}{c}13 \\ 13-k+i\end{array}\right]\) and \(A_{4}-A_{3}=190 \mathrm{p}\), then \(p\) is equal to :

1. A \(50\)
2. B \(51\)
3. C \(48\)
4. D \(49\)