  We study the necessary conditions for bosons composed of two distinguishable
fermions to exhibit bosonic-like behaviour. We base our analysis on tools of
quantum information theory such as entanglement and the majorization criterion
for probability distributions. In particular we scrutinize a recent interesting
hypothesis by C. K. Law in the Ref. Phys. Rev. A 71, 034306 (2005) that
suggests that the amount of entanglement between the constituent fermions is
related to the bosonic properties of the composite boson. We show that a large
amount of entanglement does not necessarily imply a good boson-like behaviour
by constructing an explicit counterexample. Moreover, we identify more
precisely the role entanglement may play in this situation.
