A partition of size $n$ is a (finite) sequence of positive integers of sum $n$. The Plancherel measure on the set of partitions of size $n$ is a probabliity measure that comes from the representation theory of the symmetric group. To each partition one can associate its core: it is a certain subpartition, which namely comes up in the representation theory and which can be defined from the descent set of the underlying partition. In a recent work, we proved that, under the Plancherel measure and after renormalisation, the size of the core converges in distribution to a sum of independent Gamma distributions with explicit parameters. The proof relies on the fact that the descent set of a partition is a determinantal point process (Borodin-Okounkov-Olshanki). We then use a central limit theorem of Costin-Lebowitz and Soshnikov for such processes.