  Bhargava has given a formula, derived from a formula of Serre, computing a
certain count of extensions of a local field, weighted by conductor and by
number of automorphisms. We interpret this result as a counting formula for
permutation representations of the absolute Galois group of the local field,
then speculate on variants of this formula in which the role of the symmetric
group is played by other groups. We prove an analogue of Bhargava's formula for
representations into a Weyl group in the B_n series, which suggests a link with
integration on p-adic groups. We also obtain analogous positive results in odd
residual characteristic, and negative results in residual characteristic 2, for
the D_n series (in the appendix) and the exceptional group G_2.
