Lesson5.pdf - 2013 JKUAT SODeL JOMO KENYATTA UNIVERSITY OF AGRICULTURE TECHNOLOGY JJ II J I J DocDoc I Back Close SCHOOL OF OPEN DISTANCE AND eLEARNING

Lesson5.pdf - 2013 JKUAT SODeL JOMO KENYATTA UNIVERSITY OF...

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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close JOMO KENYATTA UNIVERSITY OF AGRICULTURE & TECHNOLOGY SCHOOL OF OPEN, DISTANCE AND eLEARNING P.O. Box 62000, 00200 Nairobi, Kenya E-mail: [email protected] SMA 2104 Mathematics for Sciences LAST REVISION ON May 10, 2013
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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close SMA 2104 Mathematics for Sciences This presentation is intended to covered within one week. The notes, examples and exercises should be supple- mented with a good textbook. Most of the exercises have solutions/answers appearing elsewhere and accessible by clicking the green Exercise tag. To move back to the same page click the same tag appearing at the end of the solu- tion/answer. Errors and omissions in these notes are entirely the re- sponsibility of the author who should only be contacted through the Department of Curricula & Delivery (SODeL) and suggested corrections may be e-mailed to [email protected] . JKUAT: Setting trends in higher Education, Research and Innovation 0
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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close SMA 2104 Mathematics for Sciences LESSON 5 Permutations and Combination 5.1. Permutations This is defined as the number of different ways of arranging different objects in order. 5.1.1. Factorial notation Let n be a positive integer,then a factorial notation denoted n ! is given by n ! = n × ( n - 1) × ( n - 2) × ............. × 2 × 1 Remark. 0! = 1 and 1! = 1 JKUAT: Setting trends in higher Education, Research and Innovation 1
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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close SMA 2104 Mathematics for Sciences 5.1.2. Relationship between Factorial and Permutation Let n be the number of different objects. If repetitions are not allowed then;- 1. The number of different ways of arranging the objects in order is n ! 2. The number of ways of selecting r objects from n objects in order is given by n P r = n ! ( n - r )! , n permutations r Remark. If repetitions are allowed, the number of different ways of selecting r objects from n objects is equal to n r Number of different ways of arranging n objects in order if r JKUAT: Setting trends in higher Education, Research and Innovation 2
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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close SMA 2104 Mathematics for Sciences objects are the same is given by n !
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