Mathematics in Ancient and Medieval India c7.s3.1

c7.s3.1

Smith⁵ opined that "the Hindus seem to have given no attention to permutation and combination until Bhāskara II took it up in his *Līlāvatī*". Chakravarty⁶ has shown that the subject of permutations and combinations is a noteworthy contribution of the Indians and its interest originated before the Christian era. A summary is also given by Srinivasienger.¹ In the early Jain canonical literature, permutation was termed *Vikalpa-gaṇita* and combination *Bhaṅga*. The Jain *Bhagavatī-sūtra* (300 B. C.) calculated the number of combinations of n fundamental categories taken two at a time, three at a time, and so on.² Suśruta (200 B. C.) correctly gave the sum of the combinations of six tastes taken one at a time, two at a time etc. upto all at a time.³ Varāhamihira⁴ (505 A. D.) has stated that "an immense number of perfumes can be made from sixteen substances taken in one, two, three or four proportions and has correctly given the number of perfumes resulting from 16 ingredients (being mixed in all proportions) as 174720". The results given agree with the modern formulae though there is no mention of any such formula in his text.