Combinations and Permutations What's the Difference? In English we use the word "combination" loosely, without thinking if the order of things is important. In other words: |[pic] |"My fruit salad is a combination of apples, grapes and bananas" We don't care what order the fruits are in, they could also be | | |"bananas, grapes and apples" or "grapes, apples and bananas", its the same fruit salad. | | |
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Combinations and Permutations What's the Difference? In English we use the word "combination" loosely, without thinking if the order of things is important. In other words: |[pic] |"My fruit salad is a combination of apples, grapes and bananas" We don't care what order the fruits are in, they could also be | | |"bananas, grapes and apples" or "grapes, apples and bananas", its the same fruit salad. | | |
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Factorials, Permutations and Combinations Factorials A factorial is represented by the sign (!). When we encounter n! (known as 'n factorial') we say that a factorial is the product of all the whole numbers between 1 and n, where n must always be positive. For example 0! is a special case factorial. This is special because there are no positive numbers less than zero and we defined a factorial as a product of the numbers between n and 1. We say that 0! = 1 by claiming that the product of no numbers
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Page |1 PERMUTATIONS and COMBINATIONS If the order doesn't matter, it is a Combination. If the order does matter it is a Permutation. PRACTICE! Determine whether each of the following situations is a Combination or Permutation. 1. Creating an access code for a computer site using any 8 alphabet letters. 2. Determining how many different ways you can elect a Chairman and Co-Chairman of a committee if you have 10 people to choose from. 3. Voting to allow 10 new members to join a club when there are
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Week 1 DQ 1 Response 1) Given the enumeration methods; sum rule, product rule, permutations, combinations along with enumeration methods for indistinguishable objects, how can we devise a strategy to solve problems requiring these methods? A basic concept in the branch of the theory of algorithms called enumeration theory, which investigates general properties of classes of objects numbered by arbitrary constructive objects (cf. Constructive object). Most often, natural numbers appear in the role
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permutation In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting (rearranging) objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order. For example, there are six permutations of the set {1,2,3}, namely (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). One might define an anagram of a word as a permutation of its letters. The study of permutations
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techniques that involve permutations and combinations are helpful when calculating theoretical probabilities. This section will examine methods for determining theoretical probabilities of successive or multiple events. Permutation? or Combination? The following flow chart will help determine which formula is suitable for any given question. By simply following a series of "yes" or "no" questions, the appropriate formula can be determined. Flow Ex. 1 - Using Permutations: 6.3 Probabilities
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nature and experience must be made the starting points in planning and organizing school programs. Steps of the Integration Method. Subject: Probability Topic: Permutations and combinations 1. Introduction of the unit. Start off by explaining the objectives. After that, the teacher will present a pre-test about permutation that should be answered before the class ends. The teacher should correlate the lesson to the past lessons
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time? 5 *4*3= 60 ways This is permutation of n different thing taken r at a time 60=(5*4*3*2*1)/(2*1) = 5!/2!=5!(5-3)!=n!/(n-r)! We are talking about linear arrangement not the circular one here nPr= filling r places by n different thing n=5 {A,B,C,D,E} r=3 {A,B,C}, {A,B,D}, {A,C,D}, {A,C,E}………….. [Note: Arrangement is related to permutation. If we are considered about place or position it is permutation question. Selecting is related to permutation. If we are not considered about place
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700+ GMAT Problem Solving Probability and Combinations Questions With Explanations Collected by Bunuel Solutions by Bunuel gmatclub.com 1. Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his? A. 24/64 B. 32/64 C. 36/64 D. 40/64 E. 42/64 Expected value of a roll of one dice is 1/6(1+2+3+4+5+6)=3.5. Expected value of three dices is 3*3.5=10.5. Mary scored
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