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Permutations and Combinations

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sanford
11 diapositives · 951 Views · Aug 27, 2012

CSE 2813 Discrete Structures. Permutations. Permutation: A set of distinct objects in an ordered arrangement of these objects.r-permutation: An ordered arrangement of r elements of a set.Example: Consider the set S = {1,2,3}.What are the 3-permutations of S ?What are the 2-permutations of S ?.

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Permutations and Combinations
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    1. CSE 2813 Discrete Structures Permutations and Combinations Section 5.3

    2. CSE 2813 Discrete Structures Permutations Permutation: A set of distinct objects in an ordered arrangement of these objects. r-permutation: An ordered arrangement of r elements of a set. Example: Consider the set S = {1,2,3}. What are the 3-permutations of S ? What are the 2-permutations of S ?

    3. CSE 2813 Discrete Structures Permutations The number of r-permutations of an n-element set is:

    4. CSE 2813 Discrete Structures Example How many different ways are there to select 4 different players from 10 players on a team to play four tennis matches, where the matches are ordered?

    5. CSE 2813 Discrete Structures Example Suppose that there are eight runners in a race. Gold, silver and bronze medals are given. How many different ways are there to award these medals, if all possible outcomes of the race can occur?

    6. CSE 2813 Discrete Structures Example Suppose that a saleswoman has to visit eight different cities. She must begin her trip in a specified city, but she can visit the other seven cities in any order she wishes. How many possible orders can the sales woman use when visiting these cities?

    7. CSE 2813 Discrete Structures Combinations r-combination: An unordered selection of r elements of a set. Example: Consider the set S = {1,2,3}. What are the 2-combinations of S ?

    8. CSE 2813 Discrete Structures Combinations The number of r-combinations of an n-element set, where 0 ? r ? n, is:

    9. CSE 2813 Discrete Structures Example How many ways are there to select 5 players from a 10 member tennis team to make a trip to a match at another school?

    10. CSE 2813 Discrete Structures Example A committee has to be selected to develop a discrete mathematics course at a school. The committee is to consist of 3 faculty members from the mathematics department and 4 from the computer science department. There are 9 faculty members in the mathematics department and 11 in the computer science department. How many ways are there to select the committee?

    11. CSE 2813 Discrete Structures Summary