  In this article we state and prove a dichotomy, which is satisfied by the
number of non-singleton blocks in Lambda-coalescents which have a dust
component.
  The dichotomy is of a similar type to two well known results, also
dichotomies in the behaviour of the Lambda-coalescent, of Pitman (1999) and
Schweinsberg (2000). The three dichotomies combine together to give a complete
picture of the qualitative behaviour of the singleton/non-singleton blocks of
the Lambda-coalescent.
