Question

The number of points $(x,y,z)$ in space, whose each coordinate is a negative integer such that $x+y+z+12=0,$ is

• A. $385$
• B. $55$
• C. $110$
• D. none of these

Answer 1

The correct option is B $55$

Let $x=1,y=1$ Then the number of ordered pairs will be 10.
$x=2,y=1$ then the number of ordered pairs will be 9
And so on...
The required number of ways is
${}^{12-1}{C}_2$
$={}^{11}{C}_2$
$=\frac{11\times 10}{2}$
$=55$