As it is well-known, the number of colorings of a knot diagram by a finite quandle is a knot invariant, and using the theory of quandle (co)homology, we have a better knot invariant called the quandle cocycle invariant. The author generalizes the coloring (counting) and cocycle invariants for finite racks. A key observation is that for a finite rack \((R,\triangleleft)\), there is a positive integer \(N(R)\) called the rack rank, such that the \(N(R)\)-times iterates of \(\triangleleft \, x:R \rightarrow R\) is trivial for all \(x \in R\). This implies that the number of \(R\)-colorings only depends on the blackboard framing modulo \(N(R)\), so by suitably modifying the way of counting we get a knot invariant.