The probability distribution functions P-s(r) of the distance r between the end points of subchains of a single excluded volume chain in two and three dimensions were studied using the bond-fluctuation model. The index s refers to three principle cases. Case s=0 : the subchain is identical to the whole chain. Case s=1 : the subchain constitutes one extremity of the whole chain. Case s=2 : the subchain belongs to the central part of the whole chain. It is shown that the data can be described by the functions f(s)(x) similar to x(theta s) for small x and f(s)(x) similar to x(kappa s) exp(- D(s)x(delta s)) for large x, x being the scaled distance. All exponents theta(s), kappa(s), and delta(s) were calculated and compared with existing values in the literature. In two dimensions a crossover between theta(s) and kappa(s) was detected whereas in three dimensions theta(s) similar or equal to kappa(s) within statistical errors.