We study different ways of determining the mean distance (r[subscript n]) between a reference point and its nth neighbour among random points distributed with uniform density in a D-dimensional Euclidean space. First, we present a heuristic method; though this method provides only a crude mathematical result, it shows a simple way of estimating (r[subscript n]). Next, we describe two alternative means of deriving the exact expression of (r[subscript n]): we review the method using absolute probability and develop an alternative method using conditional probability. Finally, we obtain an approximation to (r[subscript n]) from the mean volume between the reference point and its nth neighbour and compare it with the heuristic and exact results.