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Chapter Permutations and Combinations CoNnTENTS Permutations 5.1 The factorial 5.2 Exponent of prime p inn! 5.3 | Fundamental principles of counting 5.4 Definition of permutation 5.5 | Number of permutations without repetition 5.6 Number of permutations with repetition 5.7 Conditional permutations 5.8 Circular permutations Combinations 5.9 Definition 5.10 | Number of combinations without repetition 5.11 | Number of combinations with repetition and all possible selections 5.12 | Conditional combinations 5.13 | Division into groups 5.14 | Derangement 5.15 | Some important results for geometrical problems 5.16 | Multinomial theorem 5.17 | Number of divisors Assignment (Basic and Advance Level) Answer Sheet of Assignment Bhaskaracharya Tre concepts of permutations and combinations can be traced back to the advent of Jainism in India and perhaps even earlier. Among the Jains, Mahavira, (around 850 A.D.) is perhaps the world's first mathematician credited with providing the general formulae for permutations and combinations. Bhaskaracharya (born 1114 A.D.) treated the subject matter of permutations and combinations under the name Anka Pasha in his famous work Lilavati. In addition to the general formulae for "C, and "P, already provided by Mahavira, Outside India, the subject matter of permutations and combinations had its humble beginnings in China in the famous book I-King (Book of changes). The first book which gives a comkplete treatment of the subject matter of permutations and combinations is Ars conjectandi written by a Swiss, Jacob Bernouli (1654-1705 A.D.) posthumously published in 1713 A.D. This book contains essentially the theory of permutations and combinations as is known today. 
