PPT-Tractable Combinations

of Global Constraints CP 2013 pp 230246 Authors Cohen Jeavons Thornstensen Zivny Presented by Robert Woodward Disclaimer Some slides and images borrowed from the authors own slides at CP 2013. Mr. Mark Anthony Garcia, M.S.. Mathematics Department. De La Salle University . Experiment: Definition. An . experiment . is a process that generates a set of data. .. Example 1: . Experiment. Tossing of a coin. Permutations with Repetition. Theorem 1: . The number of . r-permutations. of a set of . n. objects with repetition allowed is . n. r. . .. Example 1:. How many strings of length . r. can be formed from the English alphabet?. Statistics group. Axelborg. 16/01 2012. Anders . Stockmarr,. DTU Data Analysis. Joint work with . Peter Heegaard . and . Nanna Skall Sørensen. Acute Phase Proteins – APP’s:. Proteins whose plasma concentrations . Generating Permutations. Many different algorithms have been developed to generate the n! permutations of this set.. We will describe one of these that is based on the . lexicographic . (or . dictionary. MAP . Problems. Probabilistic. Graphical. Models. Inference. Correspondence /data association. Find highest scoring matching. maximize . . ij. . ij. . X. ij. subject to mutual exclusion constraint. Other Counting Tools: Factorials. MATH 110 Sec 12-3 Lecture: Permutations and Combinations . Other Counting Tools: Factorials. Sometimes we are interested in counting the number of different arrangements of a group of objects.. Section . 6.5. Permutations with Repetition. Theorem . 1. : The number of . r. -permutations of a set of . n. objects with repetition allowed is . n. r. .. . Example. : How many strings of length . Evaluate the following. 6!. MATH 110 Sec 12.3 Permutations and Combinations Practice Exercises . Evaluate the following. 6! = 6 x 5 x 4 x 3 x 2 x 1. MATH 110 Sec 12.3 Permutations and Combinations Practice Exercises . Section 6.. 2. The Pigeonhole Principle. If a flock of . 20. pigeons roosts in a set of . 19 . pigeonholes, one of the pigeonholes must have more than . 1. pigeon.. Pigeonhole Principle. : If . And the impossibility of utility maximisation. From indifference…. Concept of subjective utility dates back at least to Aristotle; made central tenet of economics and philosophy by Jeremy Bentham (. Evaluate the following. (7-3)! . 6! . MATH 110 Sec 12.3 Permutations and Combinations Practice Exercises . Evaluate the following. . = . . . = . . .  .  . . MATH 110 Sec 12.3 Permutations and Combinations Practice Exercises . M11.E.3.2.1: Determine the number of permutations and/or combinations or apply the fundamental counting principle. Objectives. Permutations. Combinations. Vocabulary. A . permutation. is an arrangement of items in a particular order.. Random Things to Know. Dice. . (singular = “die”). Most cases: 6 sided. Numbers 1,2,3,4,5,6. Special Cases: . 4 sided. 8 sided. 10 sided. 12 sided. 20 sided.  . Random Things to Know. Cards. Typical Deck: 52 cards. 4. Compute the number of combinations of . n. individuals taken . k. at a time.. Use . combinations to calculate probabilities.. Use . the multiplication counting principle and combinations to calculate probabilities..