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Let n k denotes nCk and n k n k if0 le k le n 0 otherwi: (Mathematics) | DivineJEE

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Mathematics

Exam

Mathematics

Let

\binom{n}{k}

denote

^nC_k

and let:

\left[ \begin{matrix} n \\ k \end{matrix} \right] = \begin{cases} \binom{n}{k}, & \text{if } 0 \le k \le n \\ 0, & \text{otherwise} \end{cases} \\ \text{If } A_k = \sum_{i=0}^{9} \binom{9}{i} \left[ \begin{matrix} 12 \\ 12-k+i \end{matrix} \right] + \sum_{i=0}^{8} \binom{8}{i} \left[ \begin{matrix} 13 \\ 13-k+i \end{matrix} \right] \\ \text{and } A_4 - A_3 = 190p,

then p is equal to

\_\_\_\_\_\_\_\_\_

.

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