| Title: | Permutation |
| Original Title: | Alternation |
| Volume and Page: | Vol. 1 (1751), p. 304 |
| Author: | Jean-Baptiste le Rond d'Alembert (biography) |
| Translator: | Richard J. Pulskamp [Xavier University] |
| Original Version (ARTFL): | Link |
| Source: | Originally published at http://www.cs.xu.edu/math/Sources/Dalembert/ ; used by permission |
| Rights/Permissions: |
This text is protected by copyright and may be linked to without seeking permission. Please see http://quod.lib.umich.edu/d/did/terms.html for information on reproduction. |
| URL: | http://hdl.handle.net/2027/spo.did2222.0001.111 |
| Citation (MLA): | d'Alembert, Jean-Baptiste le Rond. "Permutation." The Encyclopedia of Diderot & d'Alembert Collaborative Translation Project. Translated by Richard J. Pulskamp. Ann Arbor: Michigan Publishing, University of Michigan Library, 2009. Web. [fill in today's date in the form 18 Apr. 2009 and remove square brackets]. <http://hdl.handle.net/2027/spo.did2222.0001.111>. Trans. of "Alternation," Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, vol. 1. Paris, 1751. |
| Citation (Chicago): | d'Alembert, Jean-Baptiste le Rond. "Permutation." The Encyclopedia of Diderot & d'Alembert Collaborative Translation Project. Translated by Richard J. Pulskamp. Ann Arbor: Michigan Publishing, University of Michigan Library, 2009. http://hdl.handle.net/2027/spo.did2222.0001.111 (accessed [fill in today's date in the form April 18, 2009 and remove square brackets]). Originally published as "Alternation," Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, 1:304 (Paris, 1751). |
Permutation, is said sometimes in order to express the change of order which one can give to many things or to many persons, in the successive placement of them, the one after the other, or the one before the other. Thus three letters a, b, c , can incur an alternation in six different ways; abc, acb, bac, bca, cba, cab.
The permutation is one of the different kinds of combinations. See Combination. Here is the rule. In order to find all the possible permutations of a number of given things, for example of five things, (as of five letters, of five persons, etc.) take all the numbers from unity to five, and multiply them successively the one by the other, 1 by 2, then by 3, then by 4, then by 5, the product 120 will be the number of permutations sought.
The reason for this practice is very simple. Take for example two letters a and b , it is evident that there are only two possible permutations , ab , ba ; take a third letter c , it is evident that this third letter can be arranged in three different ways in each of the two preceding permutations; namely, either at the head, or in the middle, or at the end. There are therefore for three letters two times three permutations or six. Take a fourth letter, it can likewise occupy four different places in each of the six permutations of three letters, this which makes six times 4 or 24; likewise five letters will make twenty-four times 5 or 120, and thus in sequence.