  In this talk we shall show our recent results in understanding the spin$^{\rm
parity}$ 0$^+$ ground state (0 g.s.) dominance of many-body systems. We propose
a simple approach to predict the spin $I$ g.s. probabilities which does not
require the diagonalization of a Hamiltonian with random interactions. Some
findings related to the 0 g.s. dominance will also be discussed.
