  We study a many-body mixture of an equal number of bosons and two-component
fermions with a strong contact attraction. In this system bosons and fermions
can be paired into composite fermions. We construct a large N extension where
both bosons and fermions have the extra large N degrees of freedom and the
boson-fermion interaction is extended to a four-point contact interaction which
is invariant under the O(N) group transformation, so that the composite
fermions become singlet in terms of the O(N) group. It is shown that such O(N)
singlet fields have controllable quantum fluctuations suppressed by 1/N factors
and yield a systematic 1/N-expansion in terms of composite fermions. We derive
an effective action described by composite fermions up to the
next-to-leading-order terms in the large N expansion, and show that there can
be the BCS superfluidity of composite fermions at sufficiently low
temperatures.
