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We propose a strategy that optimally schedules and allocates users for adaptive modulation and coding based orthogonal frequency multiple access systems (AMC-OFDMA). This strategy aims to maximize the average system throughput as a function of bit error rate (BER) and spectral efficiency by exploiting the user diversity. It sorts the available users of an assigned base station (BS) in queues based on their priority levels and optimally selects a user from each queue, in which the average system throughout is maximized. Moreover, the proposed strategy guarantees fair services for all users in distinct priority levels. The scheduled users are allocated over the utilized bands in an optimal manner in order to improve the performance of the investigated system. Each user selects a suitable modulation and coding scheme (MCS) based on the corresponding minimum signal-to-noise ratio (SNR). The sub-carriers of the transmitted OFDMA frame are grouped in different bands depending on the number of utilized priority levels in a BS. Simulation results show the performance improvement obtained by the proposed strategy over other compared schemes.