Finding the maximum possible volume of a tetrahedron

Suppose I have three vectors $\overline{x}=a\hat{i}+b\hat{j}+c\hat{k}$, $\overline{y}=b\hat{i}+c\hat{j}+a\hat{k}$, $\overline{z}=c\hat{i}+a\hat{j}+b\hat{k}$, where we can choose a, b, c from the set {1,2,3,....13}. We have to find the probability of the tetrahedron formed by $\overline{x}$, $\overline{y}$, $\overline{z}$ having maximum volume. How should I maximise the determinant for finding the maximum possible volume of the resulting tetrahedron? Can someone help me figure this out?

Suppose I have three vectors $\overline{x}=a\hat{i}+b\hat{j}+c\hat{k}$, $\overline{y}=b\hat{i}+c\hat{j}+a\hat{k}$, $\overline{z}=c\hat{i}+a\hat{j}+b\hat{k}$, where we can choose a, b, c from the set {1,2,3,....13}. We have to find the probability of the tetrahedron formed by $\overline{x}$, $\overline{y}$, $\overline{z}$ having maximum volume. How should I maximise the determinant for finding the maximum possible volume of the resulting tetrahedron? Can someone help me figure this out?