The number of integral solutions of x+y+z=0 with x≥−5,y≥−5,z≥−5 is
The correct option is C 136
Let x=p−5,y=q−5 and z=r−5, where p,q,r≥0.
Then the given equation reduces to p+q+r=15⋯(1)
Now, we have to find non-negative integral solution of Eq. (1).
The total number of such solutions is 15+3−1C3−1= 17C2=136.