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My understanding is that some of the earliest references to applied combinatorics come from Vedic sources, for instance the Ayurvedic medical treatises of Charaka and Sushruta.

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Yes, Hindu scripture does contain combinatorics.. Here is what N.L. Biggs says in this excerpt from his journal paper "The Roots of Combinatorics":

It seems that, from a very early time, the Hindus became accustomed to considering questions involving permutations and combinations. A typical example occurs in the medical treatise of Susruta... In chapter LXIII ... We find a discussion of the various kinds of taste which can be made by combining six basic qualities: sweet, acid, saline, pungent, bitter, and astringent. There is a systematic list of combinations: six taken separately, fifteen in twos, twenty in threes, fifteen in fours, six in fives, and one taken all together.

Biggs is referring to this chapter of the Sushruta Samhita, an important Ayurvedic text. And the chapter does indeed count the number of combinations obtained taking each tastes individual, combining two together, combining three together, etc.

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