$$ \sum\limits_{k=1}^n k(k+1)(k+2) \ldots(k+r-1)= $$

If $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 1 & 3 & 5 \\ 2 & 1 & 6\end{array}\right]$ and $|\operatorname{adj}(\operatorname{adj} A)|(\operatorname{adj} A)^{-1}=k A$, then $k=$

If the values $x=\alpha, y=\beta, z=\gamma$ satisfy all the 3 equations $x+2 y+3 z=4,3 x+y+z=3$ and $x+3 y+3 z=2$, then $3 \alpha+\gamma=$

The number of solutions of the system of equations $2 x+y-z=7, x-3 y+2 z=1, x+4 y-3 z=5$ is