The probability distribution of the total transmission is studied for waves multiply scattered from a random, static configuration of scatterers. A theoretical study of the second and third cumulants of this distribution is presented. Within a diagrammatic approach a theory is developed that relates the third cumulant normalized to the average, 〈〈Ta3〉〉 to the normalized second cumulant 〈〈Ta2〉〉. For a broad Gaussian beam profile, it is found that 〈〈Ta3〉〉=16/3〈〈Ta2〉〉2. This is in good agreement with data of optical experiments.