  In this paper, we compute the number of general points through which a
general Brill-Noether curve in $\mathbb{P}^4$ passes. We also prove an
analogous theorem when some points are constrained to lie in a transverse
hyperplane. As explained in arXiv:1809.05980, these results play an essential
role in the first author's proof of the Maximal Rank Conjecture.
