Binomial Theorem

Let \(\left( {\matrix{ n \cr k \cr } } \right)\) denotes \({}^n{C_k}\) and \(\left[ {\matrix{ n \cr k \cr } } \right] = \left\{ {\matrix{ {\left( {\matrix{ n \cr k \cr } } \right),} & {if\,0 \le k \le n} \cr {0,} & {otherwise} \cr } } \right.\)

If \({A_k} = \sum\limits_{i = 0}^9 {\left( {\matrix{ 9 \cr i \cr } } \right)\left[ {\matrix{ {12} \cr {12 - k + i} \cr } } \right] + } \sum\limits_{i = 0}^8 {\left( {\matrix{ 8 \cr i \cr } } \right)\left[ {\matrix{ {13} \cr {13 - k + i} \cr } } \right]}\) and A₄ \(-\) A₃ = 190 p, then p is equal to :