Extrinsic semiconductors

An n-type semiconductor is made by doping with pentavalent atoms. Electrons are the majority carriers and holes are the minority carriers.

Indium is a trivalent impurity (acceptor); it creates holes, so the doped semiconductor is p-type.
For a semiconductor in thermal equilibrium, $n_en_h = n_i^2$ (mass action law).
$n_i = 1.5\times10^{16}\ m^{-3}$, so $n_i^2 = 2.25\times10^{32}\ m^{-6}$
$n_e = \frac{n_i^2}{n_h} = \frac{2.25\times10^{32}}{4.5\times10^{22}}$
$n_e = 0.5\times10^{10} = 5\times10^9\ m^{-3}$
So it is p-type with electron concentration $n_e = 5\times10^9\ m^{-3}$.

Antimony is a pentavalent element (5 valence electrons); germanium is tetravalent.
Four of the electrons of antimony form covalent bonds with neighbouring germanium atoms and the fifth electron is donated as a free electron.
So antimony is a donor atom and the crystal becomes an n-type semiconductor.
In an n-type semiconductor electrons are the majority carriers, so there are more free electrons than holes.
Doping increases the number of charge carriers, so the resistance decreases, not increases.
Hence there will be more free electrons than holes in the semiconductor.