  Let G be a pi-separable group with a Hall pi-subgroup H or order n. For x in
H let lambda(x) be the number of Hall pi-subgroups of G containing x. We show
that $\prod_{d\mid n}\prod_{x\in H}\lambda(x^{d})^{\frac{n}{d}\mu(d)}=1$, where
mu is the M\"obius function. This generalizes fixed point formulas for coprime
actions by Brauer, Wielandt and Navarro-Rizo. We further investigate an
additive version of this formula.
