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A new approach to the classical fixed-length noiseless source coding problem is proposed for the case of finite ergodic Markov sources. This approach is based on simple counting arguments. The central notion of "Markov type" (a set containing all the source sequences having the same transition counts from letter to letter) is introduced and the cardinality of such a set is evaluated via graph theoretical tools. The error exponent is shown to be a weighted average of informational divergences, and the universal character of the result is stressed. As a corollary, the classical source coding theorem (determining the achievable rates) is rederived.