= Solution
For equal internal degeneracy, the <number density> of an isotropic ultrarelativistic species is proportional to
$$
\int_0^\infty\frac{p^2\,dp}{e^{\beta pc}\mp1}.
$$
With $x=\beta pc$, compare the <Fermi-Dirac distribution> and <Bose-Einstein distribution> using
$$
\frac1{e^x+1}=\frac1{e^x-1}-\frac2{e^{2x}-1}.
$$
For $s>0$, a <change of variables> in the second term gives the <fermion-to-boson thermal integral ratio>
$$
\int_0^\infty\frac{x^s\,dx}{e^x+1}
=\left(1-2^{-s}\right)
\int_0^\infty\frac{x^s\,dx}{e^x-1}.
$$
Particle number has $s=2$, so $n_f=(1-2^{-2})n_b=3n_b/4$. The <energy density> contains one further factor $E=pc$, so it has $s=3$ and
$$
\rho_f=(1-2^{-3})\rho_b=\frac78\rho_b.
$$
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