Let \(\left(\begin{matrix}n \\ k\end{matrix}\right)\) denote \({}^{n}C_{k}\) and \(\left[\begin{matrix}n \\ k\end{matrix…

Let \(\left(\begin{matrix}n \\ k\end{matrix}\right)\) denote \({}^{n}C_{k}\) and \(\left[\begin{matrix}n \\ k\end{matrix}\right]=\left{\begin{matrix}\left(\begin{matrix}n \\ k\end{matrix}\right),\text{ if }0\leq k\leq n \\ 0,\text{ otherwise }\end{matrix}\right.\)

If \({A}_{k}=\sum _{i=0}^{9}\left(\begin{matrix}9 \\ i\end{matrix}\right)\left[\begin{matrix}12 \\ 12-k+i\end{matrix}\right]+\sum _{i=0}^{8}\left(\begin{matrix}8 \\ i\end{matrix}\right)\left[\begin{matrix}13 \\ 13-k+i\end{matrix}\right]\)

and \({A}_{4}-{A}_{3}=190p\), then \(p\) is equal to.........

[JEE Main 2021, 26 Aug (Shift 2)]