PERMUTATIONS AND COMBINATIONS.

The concepts of permutations and combinations can be traced back to the advent of jainism in India and perhaps even earlier. The credit, howevere, goes to the jains who treated its subject matter as a self-contained topic in mathematics, under the name vikalpa. Among the jains, mahavira, (around 850) is perhaps the world's first mathematician credited with providing the general formulae for permutations and combinations. In the 6th century B.C., Sushruta, in his medicinal work, Sushruta Samhita, asserts that 63 combinations can be made out of 6 different tastes, taken one at a time, two at a time, etc. Pingala, a Sanskrit scholar around third century B.C., gives the method of determining the number of combinations of a given number of letters, taken one at a time, two at a time, etc. In his work Chhanda Sutra. Bhaskaracharya(born 1114) treated the subject matter of permutations and combinations under the name Anka Pasha in his famous work Lilavati. In mahavira, Bhaskaracharya gives several important theorems andrestl concerning the subject...