The number of integers x, y, z, w satisfying $x+y+z+w=25$ and $x,y,z\ge -1,w\ge 1$  is 
 

$$\begin{gathered} 1=x+1\ge 0 \\ \begin{array}{l}b=y+1\ge 0\\ c=z=1\ge 0\\ d=w-1\ge 0\end{array} \end{gathered}$$
$\begin{array}{l}\therefore Thegivenequationx+y+z+w=25\\ reduceto\\ \Rightarrow (a-1)+(b-1)+(-1)+(d+1)=25\\ \Rightarrow a+b+c+d=27\\ itisequal{}^{27+4-1}{C}_{4-1}={30}_{C_3}\end{array}$