For integers \(n\) and \(r\), let \(\left(\begin{array}{l}n \\ r\end{array}\right)= \begin{cases....

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For integers \(n\) and \(r\), let \(\left(\begin{array}{l}n \\ r\end{array}\right)= \begin{cases}{ }^n C_r, & \text { if } n \geq r \geq 0 \\ 0, & \text { otherwise }\end{cases}\)The maximum value of \(k\) for which the sum \(\sum_{i=0}^k\left(\begin{array}{c}10 \\ i\end{array}\right)\left(\begin{array}{c}15 \\ k-i\end{array}\right)+\sum_{i=0}^{k+1}\left(\begin{array}{c}12 \\ i\end{array}\right)\left(\begin{array}{c}13 \\ k+1-i\end{array}\right)\) exists, is equal to 📲PW App Link - https://bit.ly/YTAI_PWAP 🌐PW Website - https://www.pw.live



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