  We 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.
