  Entanglement within qubits are studied for the subspace of definite particle
states or definite number of up spins. A transition from an algebraic decay of
entanglement within two qubits with the total number $N$ of qubits, to an
exponential one when the number of particles is increased from two to three is
studied in detail. In particular the probability that the concurrence is
non-zero is calculated using statistical methods and shown to agree with
numerical simulations. Further entanglement within a block of $m$ qubits is
studied using the log-negativity measure which indicates that a transition from
algebraic to exponential decay occurs when the number of particles exceeds $m$.
Several algebraic exponents for the decay of the log-negativity are
analytically calculated. The transition is shown to be possibly connected with
the changes in the density of states of the reduced density matrix, which has a
divergence at the zero eigenvalue when the entanglement decays algebraically.
