If $^{19}C_{3r} = ^{19}C_{r+3}$, then r is equal to:

The value of $\sum^{10}_{r=0}\begin{pmatrix}10\\r\end{pmatrix}\begin{pmatrix}15\\14-r\end{pmatrix}$ is equal to

দৃশ্যকল্প-১ : ${ }^{2 n} \mathrm{P}_{3}=2 \times{ }^{n} \mathrm{P}_{4}$

দৃশ্যকল্প-২: $A={ }^{n} \mathrm{C}_{\mathrm{T}}+{ }^{n} \mathrm{C}_{\mathrm{r}-1}$

দৃশ্যকল্প-৩ : একটি বৃত্তের কেন্দ্র $(-\mathrm{g},-f)$ এবং

ব্যাসার্ধ$=\sqrt{\mathrm{g}^{2}+f^{2}-\mathrm{c}}$

$The\ value\ of \begin{pmatrix} 30 \\ 0 \end{pmatrix}\begin{pmatrix} 30 \\ 10 \end{pmatrix}-\begin{pmatrix} 30 \\ 1 \end{pmatrix}\begin{pmatrix} 30 \\ 11 \end{pmatrix}+\begin{pmatrix} 30 \\ 2 \end{pmatrix}\begin{pmatrix} 30 \\ 12 \end{pmatrix}-.....+\begin{pmatrix} 30 \\ 20 \end{pmatrix}\begin{pmatrix} 30 \\ 30 \end{pmatrix}=$

If $^{15}C_{3r} = ^{15}C_{r+3}$, then find the value of $r$: