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The Basic Rules of Counting

The Basic Rules of Counting - The basic rules of counting...

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The basic rules of counting Math 30530, Fall 2013 September 13, 2013 Math 30530 (Fall 2012) Counting September 13, 2013 1 / 12
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Basic counting rule 1 — The sum rule Sum rule 1 : if an experiment can proceed in one of two ways , with I n 1 outcomes for the first way, and I n 2 outcomes for the second, then the total number of outcomes for the experiment is n 1 + n 2 Math 30530 (Fall 2012) Counting September 13, 2013 2 / 12
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Basic counting rule 1 — The sum rule Sum rule 1 : if an experiment can proceed in one of two ways , with I n 1 outcomes for the first way, and I n 2 outcomes for the second, then the total number of outcomes for the experiment is n 1 + n 2 Example : Movie or dinner? # (screens) + # (restaurants) Math 30530 (Fall 2012) Counting September 13, 2013 2 / 12
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Basic counting rule 1 — The sum rule Sum rule 1 : if an experiment can proceed in one of two ways , with I n 1 outcomes for the first way, and I n 2 outcomes for the second, then the total number of outcomes for the experiment is n 1 + n 2 Example : Movie or dinner? # (screens) + # (restaurants) Sum rule 2 : if an experiment can proceed in one of m ways , with I n 1 outcomes for the first way, I n 2 outcomes for the second, . . . , and I n m outcomes for the m th, then the total number of outcomes for the experiment is n 1 + n 2 + . . . + n m Math 30530 (Fall 2012) Counting September 13, 2013 2 / 12
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Basic counting rule 2 — The product rule Product rule 1 : if an experiment is performed in two stages , with I n 1 outcomes for the first stage, and I n 2 outcomes for the second, REGARDLESS OF FIRST , then the total number of outcomes for the experiment is n 1 n 2 Math 30530 (Fall 2012) Counting September 13, 2013 3 / 12
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Basic counting rule 2 — The product rule Product rule 1 : if an experiment is performed in two stages , with I n 1 outcomes for the first stage, and I n 2 outcomes for the second, REGARDLESS OF FIRST , then the total number of outcomes for the experiment is n 1 n 2 Example : Movie and dinner? # (screens) × # (restaurants) Math 30530 (Fall 2012) Counting September 13, 2013 3 / 12
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Basic counting rule 2 — The product rule Product rule 1 : if an experiment is performed in two stages , with I n 1 outcomes for the first stage, and I n 2 outcomes for the second, REGARDLESS OF FIRST , then the total number of outcomes for the experiment is n 1 n 2 Example : Movie and dinner? # (screens) × # (restaurants) Product rule 2 : if an experiment is performed in m stages, with I n 1 outcomes for the first stage, and I n 2 outcomes for the second, REGARDLESS OF FIRST , . . . , and I n m outcomes for the m th, REGARDLESS OF ALL PREVIOUS , then the total number of outcomes for the experiment is n 1 n 2 . . . n m Math 30530 (Fall 2012) Counting September 13, 2013 3 / 12
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Arranging objects in a row In how many ways can n different, distinct objects be lined up in a row? Math 30530 (Fall 2012) Counting September 13, 2013 4 / 12
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Arranging objects in a row In how many ways can n different, distinct objects be lined up in a row?
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