  We study the number of collisions $X_n$ of an exchangeable coalescent with
multiple collisions ($\Lambda$-coalescent) which starts with $n$ particles and
is driven by rates determined by a finite characteristic measure $\nu({\rm
d}x)=x^{-2}\Lambda({\rm d}x)$. Via a coupling technique we derive limiting laws
of $X_n$, using previous results on regenerative compositions derived from
stick-breaking partitions of the unit interval. The possible limiting laws of
$X_n$ include normal, stable with index $1\le\alpha<2$ and Mittag-Leffler
distributions. The results apply, in particular, to the case when $\nu$ is a
beta$(a-2,b)$ distribution with parameters $a>2$ and $b>0$. The approach taken
allows to derive asymptotics of three other functionals of the coalescent, the
absorption time, the length of an external branch chosen at random from the $n$
external branches, and the number of collision events that occur before the
randomly selected external branch coalesces with one of its neighbours.
