It is given that, x,y,z≥−1 and w≥1 Now, let a=x+1≥0 b=y+1≥0 c=z+1≥0 d=w−1≥0 ∴ The given equation x+y+z+w=25 reduce to
(a−1)+(b−1)+(c−1)+(d+1)=25
⇒a+b+c+d=27 ∴ The number of required solution is same as the number of non-negative integral solutions of equation a+b+c+d=27 and it is equal to 27+4−1C4−1=30C3