Question

The number of non zero integral solution of $|x|+|y|+|z|=11$ is

• A. $624$
• B. $320$
• C. $312$
• D. $360$

Answer 1

The correct option is D $360$

$|x|+|y|+|z|=11$

The solution is non-zero integral then,

$x,y,z\ne 0$

There are ${}^{11-1}{C}_{3–1}$ ways to distribute the $11$.

Since, $x,y,z$ can be negative, we have $2^3$ ways to distribute the negative sign.

So this gives us a total number of non-zero solution $=8\cdot {(}^{10}{C}_2)=8\times \frac{10\times 9}{2}=360$