{"id":26384,"date":"2021-03-26T13:00:20","date_gmt":"2021-03-26T13:00:20","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=26384"},"modified":"2024-08-18T06:50:19","modified_gmt":"2024-08-18T06:50:19","slug":"counting-techniques-permutation-variation-and-combination","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/en\/counting-techniques-permutation-variation-and-combination\/","title":{"rendered":"Counting Techniques: Permutation, Variation, and Combination"},"content":{"rendered":"
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Counting Techniques: Permutation, Variation, and Combination<\/h1>\n

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Abstract<\/strong>
In the study of probabilities, counting techniques are fundamental tools for measuring the cardinality of the sample space and the event to be measured. In this context, the techniques of combination, variation, and permutation are the most used due to their ease of use and application in experiments with equiprobable outcomes. Through the measure of probability as a limit of relative frequencies, the probability of an event is established as a quotient of cardinalities. Therefore, the calculation of probabilities is reduced to calculating the cardinality of the sample space and of the event to be measured. In this sense, the derivation of counting techniques through experiments with equiprobable outcomes is crucial for the study of probabilities. Through the definition of variations, combinations, and permutations, the size of sets can be measured efficiently and accurately. This class will present various experiments designed with equiprobable outcomes and their sample spaces will be analyzed to introduce counting techniques. With these tools, the size of a wide variety of sets can be measured and probabilities of events in experiments with equiprobable outcomes can be calculated.<\/em><\/p>\n

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LEARNING OBJECTIVES:<\/strong>
\nUpon completing this class, the student will be able to:\n<\/p>\n

    \nRecall<\/strong> the formula of favorable cases over possible cases as a way to calculate the probability of an event.
    \nUnderstand<\/strong> the concepts of permutation, variation, and combination and their use in probability calculations.
    \nAnalyze<\/strong> and explain the relationship between the size of the sample space and the probability of an event in an experiment with equiprobable outcomes.
    \nIdentify<\/strong> situations in which counting techniques of combination, variation, and permutation can be applied in everyday life, such as in gambling and organizational problems.\n<\/ol>\n

    TABLE OF CONTENTS<\/strong>
    \nCOUNTING TECHNIQUES AND PROBABILITIES<\/strong><\/a>
    \n    DERIVATION OF COUNTING TECHNIQUES<\/strong><\/a>
    \n    EXPERIMENT 1 (AORm): ACTIVATE \u2013 RECORD IN ORDER \u2013 RESET, REPEAT m TIMES<\/a>
    \n    EXPERIMENT 2 (AOk): ACTIVATE \u2013 RECORD IN ORDER, REPEAT k TIMES<\/a>
    \n    EXPERIMENT 3 (ADk): ACTIVATE \u2013 RECORD IN DISORDER, REPEAT k TIMES<\/a><\/p>\n


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