  We consider the problem of counting commuting r-tuples of elements of the
symmetric group S_n, i.e. computing |Hom(Z^r,S_n)|. The cases r=1,2 are
well-known; a product formula for the case r=3 was conjectured by Adams-Watters
and later proved by Britnell. In this note we solve the problem for arbitrary
r.
