  In this talk I shall discuss some regularities of many-body systems in the
presence of random interactions and regularities of a single-$j$ shell for the
$J$ pairing interaction which works only when two particles are coupled to spin
$J$. I shall first explain an empirical rule to predict the spin $I$ ground
state probability.
  Then I shall present some interesting results of a single-$j$ shell under the
$J$ pairing interaction. Last I shall discuss some preliminary results of
binding energies in the presence of random two-body interactions.
