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In an Orthogonal Frequency Division Multiple Access (OFDMA) wireless network, inter-cell interference (ICI) is one of the main challenges, and is of special concern for users near the cell edge. ICI arises naturally from collisions of frequency resource assignments among neighboring base stations. An important performance parameter is the probability distribution of assignment collisions. In this paper, an exact analytical expression for the collision probability is derived for an arbitrary number of base stations with non-coordinated schedulers. The expression can be used to determine conditions under which ICI mitigation techniques may be required as well as to establish a baseline for performance comparison with ICI coordination schemes. For the important case of two base stations, the expression is particularly simple. Numerical results are presented to illustrate the analytical results.