Permutation & Combination And Their History
Permutation and combination is a very useful concept developed by the great mathematicians Pierre de Fermat and Blaise Pascal. When we come across the problems of arrangement or/and selection of various objects, the concept of permutation and combination helps us a lot. Let us take an example to understand the need for permutation and combination in our everyday lives. Suppose a marketing manager has the tedious task of filling three important positions from a group of eight equally qualified people. None of the people has had experience in working at a company level. Thus, the marketing manager decides to allow each of them to work for 15 days in each of the three positions before he makes a decision. Now, can you tell how long the positions will be filled by these people before permanent employees take their position? Here, we will have to use the concepts of permutation and combination to get our answers easily.
Permutations and its History
Permutations can be defined as the way of selecting or arranging a smaller or equal number of objects from a given group of objects in which due regard is given to the order in which the objects are arranged or selected. The history of permutations dates back to as early as 1000 BC when permutations called hexagrams were used by the Chinese in the book called Yi Jing which translates to Classic of Changes. In the book called the Book of Cryptographic Messages, Al Khalil used permutation and combination for the very first time to list Arabic alphabets with or without vowels. Bhaskara II in his book called Lilavati introduced the rule to obtain the number of permutations of n objects during 1150. In the late phases, the development in the field of permutations was carried out by mathematicians like Blaise Pascal, Pierre de Fermat, Joseph L. Lagrange, Fabian Stedman, and Evariste Galois.
Combinations and its History
Combinations can be defined as the way of selecting or arranging a smaller or equal number of objects from a given group of objects in which the order in which the objects are arranged or selected is not important. The history of combinations dates back to as early as the 16th century BCE when Egyptian mathematicians employed it to solve various problems. We can find the first recorded use of combinations in the Rhind Papyrus. During 300 BC, Greek mathematician Plutarch used combinations to find out the different number of syllables in the Greek language. In India, various mathematicians like Pingala, Mahavira, Hemacandra, Brahmagupta, and Bhaskara I developed various concepts of combinations. In the modern era, Leonardo Fibonacci developed the concepts of combinations to a great extent.
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