$\left( {\begin{array}{*{20}{c}}
n \\
{r + 1}
\end{array}} \right) + 2\left( {\begin{array}{*{20}{c}}
n \\
r
\end{array}} \right) + \left( {\begin{array}{*{20}{c}}
n \\
{r - 1}
\end{array}} \right) = \left( {\begin{array}{*{20}{c}}
{n + 2} \\
{r + 1}
\end{array}} \right)\,$ મળે
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$\mathrm{A}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{Z} \times \mathbb{Z}:(\mathrm{x}-2)^{2}+\mathrm{y}^{2} \leq 4\right\}$
$\mathrm{B}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{Z} \times \mathbb{Z}: \mathrm{x}^{2}+\mathrm{y}^{2} \leq 4\right\} $ અને
$\mathrm{C}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{Z} \times \mathbb{Z}:(\mathrm{x}-2)^{2}+(\mathrm{y}-2)^{2} \leq 4\right\}$
જો $\mathrm{A} \cap \mathrm{B}$ થી $\mathrm{A} \cap \mathrm{C}$ કુલ સંબંધની સંખ્યા $2^{\mathrm{p}}$ હોય તો $\mathrm{p}$ ની કિમંત મેળવો.