About permutational approach in geothermobarometry

 Let's assume that you have got a great number of micro-probe analyses from a small area of a sample/thin section (e.g. 10 Opx, 10 Grt, 5 Bt and 5 Pl) and are going to estimate P-T parameters using the THERMOCALC and AX programs, or by the TWQ package of R.G. Berman et al. Which combination of analyses demonstrates the "best" (the most closely-grouped) intersections of the curves? In this example, you must check 10×10×5×5=2500 possible combinations. Of course, being a good petrologist, you can easily reduce this number and select appropriate analyses resting on textural features. Though, in many cases you can not make the right choice even after such eliminations. You have to run THERMOCALC many times for each combination and compare results (i.e. perform routine and sometimes thankless job that eats time), or adjust bundle of curves more judiciously using the simple rule:

The equilibrium curve shifts to the side with increasing activities of its components

TC_Comb (as well as TWQ_Comb for the TWQ package of R. Berman and PTQ_Comb for the "classical" thermobarometry with PTQuick) provides another way which is more primitive: the program generates and tests with THERMOCALC all possible combinations of mineral analyses and builds large table of results. This table can be sorted then by the "fit" or "sdT" ("sdP") parameters to find the "best" combinations. In most cases, this automatic process saves hours (or even days and weeks in worse and unintelligent cases) if compared with performing such operations manually.
 Analysis of combinations may be helpful also in such investigations as testing of mineral compositions for deviations from equilibrium "from the point of view" of certain thermodynamic database and models of solid solutions (or just checking sensitivity of results to variations of mineral compositions in certain assemblages, if you prefer). At least, the simplest task is testing analytical data for your sample: "good intersections" may not present at all and further investigations required in this case. Anyhow, all possible diagrams are already calculated after processing of permutations – just see them, compare and decide!
 It is necessary to warn also that this method may provoke too "lazy" work-flow of PT-metry: just take a large set of analyses from the sample, load and process all of them in TC_Comb without texture analysis and be satisfied with the "best possible" combination! In fact, abandoning of the thorough texture checking (which is the first obligate step of this work) leads to serious misinterpretations and makes results insensible: in many cases, "best combinations" occur due to accidental coincidences of compositions that fit used thermodynamic model well (even if 3 or more linearly independent equilibria are present) rather than it is expected by the texture. It's better to regard texture as the primary feature and thermodynamic model as a simplified and imprecise thing. At least, final results should always be verified by the local textural relationships.