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Combinatorics and counting - Penn Math

Combinatorics and countingPer Alexandersson2p. alexanderssonIntroductionHere is a collection of counting problems. Questions and suggestionsVersion: 15th February 2021,22:26are welcome vs. independent that weaddthe counts for exclusive situations, andmultiplythe counts forindependent situations. For example, the possible outcomes of a dicethrow are exclusive:(Sides of a dice)=(Even sides)+(Odd sides)The different outcomes of selecting a playing card in a deck of cardscan be seen as a combination ofindependentchoices:(Different cards)=(Choice of color) (Choice of value).Labeled vs. unlabeled setsis a common cause for the following two problems: Count the number of ways to choose2people among4people. Count the number of ways to partition4people into sets of the first example, it is understood that the set of chosen peopleis aspecialset it is thechosen set.

combinatorics and counting 3 Overview of formulas Every row in the table illustrates a type of counting problem, where the solution is given by the formula. Conversely, every problem is a combinatorial interpretation of the formula. In this context, a group of things means an unordered set. Problem Type Formula Choose a group of kobjects from ...

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