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Math 1620 Week 1, Class 1

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by: Mariah Figueiredo

Math 1620 Week 1, Class 1 MATH 1620

Mariah Figueiredo

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Week 1 Class 1 notes on permutations
Contemporary Mathematical Ideas in Society
Wing Sze E Kam
Class Notes
25 ?




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1 review
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"Clutch. So clutch. Thank you sooo much Mariah!!! Thanks so much for your help! Needed it bad lol"
Felix Bogisich

Popular in Contemporary Mathematical Ideas in Society

Popular in Mathematics (M)

This 3 page Class Notes was uploaded by Mariah Figueiredo on Tuesday January 26, 2016. The Class Notes belongs to MATH 1620 at Rensselaer Polytechnic Institute taught by Wing Sze E Kam in Spring 2016. Since its upload, it has received 157 views. For similar materials see Contemporary Mathematical Ideas in Society in Mathematics (M) at Rensselaer Polytechnic Institute.


Reviews for Math 1620 Week 1, Class 1

Star Star Star Star Star

Clutch. So clutch. Thank you sooo much Mariah!!! Thanks so much for your help! Needed it bad lol

-Felix Bogisich


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Date Created: 01/26/16
Week1 11.1-11.2 Fundamental Counting Principle and Permutation Spring 2016 Q: What is Fundamental Counting Principle? A: M items N items Group 1 Group 2 Suppose we want to choose ONE item from each group, then the total number of choices is . Q: Can we apply Fundamental Counting Principle if we have to choose from many groups ( > 2 groups)? A: Yes!! Just multiply together the number of available items in every group. Example 1 There are 15 questions in a True/ False test, how many choices in total? Example 2 In NY state, typical license plates display three letters (from A to Z) followed by four numbers (from 0 to 9), e.g. RPI-1620, EET-1357. How many different typical license plates can be issued for this state? 1 Q: What are the significances of a permutation? A: A permutation is an ordered arrangement of items where - every item is used only once - the order of arrangement matters! Example 3 How many ways to arrange 7 of your favorite books along a shelf? n! = By definition, 0! = Example 4 A corporation has 7 members on its board of directors. In how many different ways can it elect a president, vice-president, secretary and treasurer? President Vice-president Secretary Treasurer n ! nPr▯ ▯ n n ▯1 n ▯ 2 ▯2▯1 ▯n ▯ r ! n ▯ r n ▯ r ▯1 ▯2▯1 2 Q: How to count permutations with duplicate items? A: For a word “SET”, letters can be arranged as Therefore, number of permutations of the letters is For a word “EXE”, letters can be arranged as Therefore, number of distinct permutations is Permutations of duplicate items: n ! where p, q, r are repeated items p !q !r ! For “EXE”, there are 3 letters, 2 of them are repeated, therefore Suggested HW 11.1 : # 7, 13, 19 11.2 : # 14, 16, 28, 30, 48, 51 3


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