  It is a classical result of Harper that the limiting distribution of the
number of blocks in partitions of the set $\{1, 2,..., n\}$ is normal. In this
paper, using the saddle point method we prove the normality of the limiting
distribution of the number of block pairs in set partitions of type $B_n$.
Moreover, we obtain that the limiting distribution of the number of block pairs
in $B_n$-partitions without zero-block is also normal.
