We study the number of collisions,Xn, of an exchangeable coalescent with multiple collisions (Λ-coalescent) which starts withnparticles and is driven by rates determined by a finite characteristic measure η(dx) =x−2Λ(dx). Via a coupling technique, we derive limiting laws ofXn, using previous results on regenerative compositions derived from stick-breaking partitions of the unit interval. The possible limiting laws ofXninclude normal, stable with index 1 ≤ α < 2, and Mittag-Leffler distributions. The results apply, in particular, to the case when η is a beta(a− 2,b) distribution with parametersa> 2 andb> 0. The approach taken allows us to derive asymptotics of three other functionals of the coalescent: the absorption time, the length of an external branch chosen at random from thenexternal branches, and the number of collision events that occur before the randomly selected external branch coalesces with one of its neighbours.