  We present an exact analytical solution of the fundamental systems of
quasi-one-dimensional spin-1/2 fermions with infinite repulsion for arbitrary
confining potential. The eigenfunctions are constructed by the combination of
Gireardeau's hard-core contacting boundary condition and group theoretical
method which guarantees the obtained states to be simultaneously the
eigenstates of $S$ and $S_z$ and fulfill the antisymmetry under odd
permutation. We show that the total ground-state density profile behaves like
the polarized noninteracting fermions, whereas the spin-dependent densities
display different properties for different spin configurations. We also discuss
the splitting of the ground states for large but finite repulsion.
