2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66014We study different ways of determining the mean distance $ < r_n >$ between a reference point and its $n$-th 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_n >$. Next we describe two alternative means of deriving the exact expression of $<r_n>$: we review the method using absolute probability and develop an alternative method using conditional probability. Finally we obtain an approximation to $ < r_n >$ from the mean volume between the reference point and its $n$-th neighbour and compare it with the heuristic and exact results.6 pages (REVTex4), minor changes in content, typing errors corrected, references addedProbabilityData Analysis, Statistics and Probabilitytext