Question

# The number of integral solutions of x+y+z=0 with x≥−5,y≥−5,z≥−5 is

Your Answer
A
134
Correct Answer
B
136
Your Answer
C
138
Your Answer
D
140

Solution

## The correct option is C 136Let 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.

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