  We deduce a formula enumerating the isomorphism classes of extensions of a
$\kp$-adic field $K$ with given ramification $e$ and inertia $f$. The formula
follows from a simple group-theoretic lemma, plus the Krasner formula and an
elementary class field theory computation. It shows that the number of classes
only depends on the ramification and inertia of the extensions $K/\Q_p$, and
$K(\zeta_{p^m})/K$ obtained adding the $p^m$-th roots of 1, for all $p^m$
dividing $e$.
