Let \(x\) be the number of objects to the left of the first object chosen, \(y\) the number of objects between the first and the second, \(\mathrm{z}\) the number of objects between the second and the third and \(u\) the number of objects to the right of the third objects. Then, \(x, u \geq 0 ; y, z \geq 1\) and \(x+y+z+u=n-3\). Let \(y_{1}=\) \(\mathrm{y}-1\) and \(\mathrm{z}_{1}=\mathrm{z}-1\). Then, \(\mathrm{y}_{1} \geq 0, \mathrm{z}_{1} \geq 0\) such that \(\mathrm{x}+\mathrm{y}_{1}+\mathrm{z}_{1}+\mathrm{u}=\mathrm{n}-5\). The total number of non-negative integral solutions of this equation is \({ }^{\mathrm{n}-5+4-1} \mathrm{C}_{4-1}={ }^{\mathrm{n}-2} \mathrm{C}_{3} .\)