Math 1620 Week 1, Class 1
Math 1620 Week 1, Class 1 MATH 1620
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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.
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Clutch. So clutch. Thank you sooo much Mariah!!! Thanks so much for your help! Needed it bad lol
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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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