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Topic: Permutations and combinations

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	CSCE 235 Discrete Math Project-Permutations and Combinations
		Combinations ask the question "How many sets of size r can be made when picking from a set of size n?" Combinations also have a notation; C(n, r), and a theorem that helps to compute C(n, r).
		If a permutation is taken from the same a set of objects, and no object in the permutation is in the same place that it was in the original arrangment, it is known as a derangement of the original order.
		For instance, the permutation 36972 is a derangement of 23697.
	www.nebraskaroads.com /csce235/section4_3_1.html (907 words)

	Permutations and combinations - Wikipedia, the free encyclopedia
		In familiar terms, a combination is an un-ordered selection made from a group of objects.
		Both combinations and permutations have variants where some objects appear more than once (that is, they have some repetition).
		Combinations and Permutations with derivation and examples from Math Is Fun
	en.wikipedia.org /wiki/Permutations_and_combinations (827 words)

	Permutations #2 (w/Combinations)
		It adds combinations to the permutations from the previous program and it adds the ability to generate permutations and combinations for subsets of objects.
		To generate all permutations for R objects from a set of N, the main change in the Setup routine to calculate the count as described above and to change the upper limit on size from N to R in the calculation routine.
		BigCombos, a unit using the Big Integers unit to generate permutations and combinations for large numbers is in the works.
	www.delphiforfun.org /Programs/Permutes_2.htm (682 words)

	Probability Concepts - PERMUTATIONS AND COMBINATIONS
		A permutation of n distinct objects taken r at a time is a subset, with r elements, of the n distinct objects.
		While order is still considered, a circular permutation is not considered to be distinct from another unless at least one object is preceded or succeeded by a different object in both permutations.
		This equality states that the number of permutation of n distinct objects taken r at a time is equal to the number of combinations of n distinct objects taken r at a time multiplied by the number of permutations of r objects (taken r at a time).
	library.thinkquest.org /10030/4pcpac.htm (679 words)

	MarbleMice.com » Blog Archive » Permutations and Combinations
		Having a basic understanding of permutations and combinations can be a very useful for programmers as it lets you quickly determine whether an easy to program brute force method will work within a reasonable time or that you need to spend time developing better algorithms to account for the large number of possible situations.
		Permutations take the position into account when looking for a unique ordering; each unique ordering is called a permutation.
		Combinations differ from permutations by ignoring the positions that the characters appear in the sequence, ‘cab’, ‘abc’ and so on are all the same combination.
	marblemice.com /2006/09/04/permutations-and-combinations (966 words)

	Permutations and Combinations (Site not responding. Last check: 2007-10-11)
		Permutations occur when it matters which die is a and which is a.
		Combinations occur when the order of the two dice doesn’t matter.
		Microstates are all possible permutations of the dice.
	www.cord.edu /faculty/ulnessd/legacy/fall99/john/tsld005.htm (42 words)

	Permutations and Combinations (Site not responding. Last check: 2007-10-11)
		Permutations and combinations are sequences of items chosen from a larger list.
		A permutation is simply a combination "k choose k" - a reordering of all the available items.
		This function is capable of handling even very large combinations (we've tested drawing from up to 100 million items, but the exact limits will depend on your available memory).
	www.sunny-beach.net /random_numbers/manual/164.htm (285 words)

	Combinatorics: Permutations, Combinations, Factorial, Exponents Generate
		Combination (N, M) = Arrangement (N, M) / Permutation (M) = {N x (N — 1) x (N — 2) x (N — 3) x x (N — M + 1)} / {1 x 2 x 3 x x M} The combinations are the equivalent of boxed arrangements.
		The combinations are the best-known element of the three mathematical entities.
		The combination, combinations are far fewer than the permutations of N numbers.
	www.saliu.com /permutations.html (2507 words)

	permutations_and_combinations_22_4.nb
		things (numbered balls, for example) in some particular order, while a combination is an arrangement without regard to order.
		If this same password is chosen so no duplicate characters are present, this is equivalent to a permutation of 26 things (letters) taken 5 at a time (length of password) but without replacement:
		Combinations are a way of selecting items from a given population but not keeping track of their order.
	www.ipr.umd.edu /~nmoody/Math/permutations_and_combinations.html (450 words)

	Permutations or Combinations (Site not responding. Last check: 2007-10-11)
		To get the answer: enter 52 in the "number of different objects" box, enter 5 in the "size of groups" box, select "Combinations" from the radio buttons at top of screen and then click "Calculate Combinations" at the bottom.
		The answer is 2598960 combinations or in other words, this hand occurs on average once in 2 million 598 hundred thousand 960 hands!
		Just as likely is a hand with the 8 of hearts, 3, 4 and jack of clubs, and 9 of spades (but you would not likely win at poker with this latter hand).
	www.wcrl.ars.usda.gov /cec/java/comb.htm (217 words)

	Permutations and combinations - Topics in precalculus
		For example, if twelve different things are permuted, then the number of their permutations is 479,001,600.
		Thus the number of permutations of 4 different things taken 4 at a time is 4!.
		This is the number of permutations of 10 different things taken 4 at a time.
	www.themathpage.com /aPreCalc/permutations-combinations.htm (1099 words)

	Permutations and combinations
		When we talk of permutations and combinations in everyday talk we often use the two terms interchangeably.
		With combinations, on the other hand, one does not consider the order in which objects were chosen or placed, just which objects were chosen.
		On combination locks you have to turn dials with numbers on so a particular number is given, e.g.
	www.mathagonyaunt.co.uk /STATISTICS/ESP/Perms_combs.html (1002 words)

	Permutations
		The permutation relationship gives you the number of ways you can choose r objects or events out of a collection of n objects or events.
		The number of permutations of r objects out of n is sometimes what you need, but it has the drawback of overcounting if you are interested in the number of ways to get distinguishable collections of objects or events.
		So the permutation relationship overcounts the number of ways to choose this combination if you don't want to make a distinction between them based on the order in which they were chosen.
	hyperphysics.phy-astr.gsu.edu /hbase/math/permut.html (485 words)

	Math Tutor: Permutations, Lawrenceville Math Science Tutor
		Now suppose you are asked to find the number of permutations that you can create from the first 9 letters of the alphabet, while only using 5 letters at a time.
		The number of combinations that can be made out of the letters A, B, and C, using all 3 letters, is only 1.
		Permutations are groupings where order DOES matter, combinations are those where order does NOT matter.
	webpages.charter.net /mgroves9/permutations.html (457 words)

	Print Combinations/Probability/Permutations (Site not responding. Last check: 2007-10-11)
		Permutation questions are about taking a group of objects and totaling how many ways we can arrange them in specific ways.
		In permutation problems, there is no divide by zero, so the zero would just be crossed out and we would multiply out 5 × 4 × 3 × 2 × 1 which equals 120.
		Use logic: combinations mean results that are the same are double counted and therefore don't count, so they need to be excluded.
	www.800score.com /permutations_problems_print.htm (7868 words)

	Probability
		Permutation illustrates the number of ways to arrange elements in a definite order.
		The number of permutations of n elements of same kind taken r at a time.
		Combination illustrates the number of ways to arrange elements without a definite order.
	www.gomath.com /algebra/probability.php (88 words)

	Probability Theory - Pascal's triangle - Combinations and Permutations
		Each of these problems is an exercise in calculating combinations, although British football pools companies and pools journalists always refer for some reason to the second example, as a permutation.
		There were 1 5 combinations, each of which could be reversed, as the combination of say, Trap 3 and Trap 4 has two orders, 3:4 and 4:3.
		It means that the number of combinations is 51 where we want to ensure we find any four from five selections in a group of ten numbers.
	www.probabilitytheory.info /topics/pascal_combinations_permutations.htm (1237 words)

	Combinations And Permutations
		With combinations and permutations we are trying to determine the number of arrangements that can be made from a set of items dividing them into specific numbers or groups.
		In permutations, the order of items is all that is important ; we count x, y, z as different from y, z, x.
		But in combinations we are concerned only that x, y and z have been selected, regardless of order; x, y, z and y, z, x are the same combination.
	www.datedial.com /datCombinations.asp (181 words)

	Ancient Jaina Mathematics: an Introduction
		A permutation is a particular way of ordering some or all of a given number of items.
		A combination is a selection from some or all of a number of items, unlike permutations, the other is not taken into account.
		Permutations and combinations were favourite topics of study among the Jainas.
	www.infinityfoundation.com /mandala/t_es/t_es_agraw_jaina.htm (1691 words)

	Permutations and combinations (2) - Topics in precalculus
		But in combinations we are concerned only that a, b, and c have been selected.
		The combinations are contained among the permutations -- they are a "subset" of the permutations.
		For, this is the sum of all possibile combinations: either no topping, or 1, or 2, and so on, up to 8.
	www.themathpage.com /aPreCalc/permutations-combinations-2.htm (1057 words)

	Permutations and Combinations
		Many problems in probability can be phrased in the language of "how many ways can we pick r objects out of a group of N objects." We now calculate the answer to this question.
		To order the r numbers chosen, we have r choices for the 1st object, r-1 choices for the 2nd object, r-2 choices for the 3rd object, and so on down until there is only 1 choice left for the last rth object.
		If we regard these N-r objects left behind as the "chosen" objects, we see that the number of combinations of N objects taken r at a time is exactly equal to the number of combinations of N objects taken N-r at a time.
	www.pas.rochester.edu /~stte/phy104-F00/notes-3.html (2570 words)

	Combination - Wikipedia, the free encyclopedia
		It has been suggested that Permutations and combinations be merged into this article or section.
		The order of the elements in a combination is not important (two lists with the same elements in different orders are considered to be the same combination).
		A combination is a special case of a partition of a set; specifically, a partition into two sets of size k and n-k.
	en.wikipedia.org /wiki/Combinations (203 words)

	NetLogo Models Library: Random Combinations and Permutations
		The model both matches each random combination against the user's secret combination and checks whether the random combination is a permutation of the original combination.
		- Distinguish between combinations and permutations and understand the implications of this distinction to the interpretation of the experimental outcomes.
		The "permutations" histogram (red) typically stretches over a greater range of values as compared to the "combination" histogram (fl).
	ccl.northwestern.edu /netlogo/models/RandomCombinationsandPermutations (2760 words)

	Stats: Counting Techniques
		Note: The difference between a permutation and a combination is not whether there is repetition or not -- there must not be repetition with either, and if there is repetition, you can not use the formulas for permutations or combinations.
		Combinations are used in the binomial expansion theorem from algebra to give the coefficients of the expansion (a+b)^n.
		Since combinations are symmetric, if n-r is smaller than r, then switch the combination to its alternative form and then use the shortcut given above.
	www.richland.edu /james/lecture/m170/ch04-not.html (782 words)

	Analysis of Algorithms: Lecture 24
		A related problem is that of generating combinations of a set of n elements taken k at a time without replacement.
		The simple (but inefficient) way to do this is just generate all possible n-bit numbers, count the bits in each, and print the corresponding combination when the number of bits is equal to k.
		Each combination that is generated is printed (unlike before), and it takes O(n) recursive invokations for each combination printed, so an upper bound on the number of recursive calls is O(n (n C k)).
	camino.rutgers.edu /ut/utsa/cs3343/lecture25.html (819 words)

	Permutations and Combinations (Site not responding. Last check: 2007-10-11)
		Permutations and Combinations are usually taught in Statistics courses and, as well, in many Algebra courses.
		C(n,r) indicates the number of combinations of n items taken r at a time.
		P(n,r) stands for the number of different permutations of n things chosen r at a time.
	fclass.vaniercollege.qc.ca /web/mathematics/real/Calculators/PermsCombs_Intro.htm (187 words)

	Duncan Williamson: Permutations and Combinations permcom.html
		A permutation is defined as being an ordered arrangement or grouping of a set of numbers, items etc and any one of a range of possible groupings, according to the Concise Oxford Dictionary.
		With the two from three subjects example, we would say that permutations 1 and 3 were equivalent to each other since they both have the numbers 1 and 2 in them.
		A combination is defined by the Concise Oxford Dictionary as a group of things chosen from a larger number without regard to their arrangement.
	www.duncanwil.co.uk /permcom.html (2064 words)

	Math Forum - Ask Dr. Math Archives: High School Permutations/Combinations
		Combinations of the Letters in a Name [03/04/1998]
		A formula for the number of combinations of the letters in a name, however many times one letter appears in that name.
		I have been trying to figure out how to arrive at the formula for calculating combinations.
	www.mathforum.org /library/drmath/sets/high_perms_combs.html (860 words)

	Math Forum: Ask Dr. Math FAQ: Permutations and Combinations
		For four-letter permutations, there are 10 possibilities for the first letter, 9 for the second, 8 for the third, and 7 for the last letter.
		we see that the total number of combinations of size 4 taken from a set of size 10 is equal to the number of permutations of size 4 taken from a set of size 10 divided by 4!.
		One of the hardest parts about doing problems that use permutations and combinations is deciding which formula to use.
	mathforum.org /dr.math/faq/faq.comb.perm.html (1035 words)

	Mass Tutor Math Statistics Homework Help Combinations and Permutations
		Permutations are used to count the number of ordered arrangements.
		In this case, P is for the permutation function and not for probability.
		When the subset of objects is taken from a larger set and the order in which these objects are arranged doesn't matter, the number of arrangements is called a combination.
	www.masstutor.net /Statistics_Homework_Help/Combinations_Permutations/statistics_homework_help_5_combinations_permutations.html (354 words)

	Working with permutations and combinations.
		If the number of permutations of n objects taken r at a time is six times the number of combinations of n objects taken r at a time, determine the value of r.
		Combinations - A person has 3 different letters to write, 2 interviews to do, and 2 commercials to review.
		Permutations and combinations - Find the number of different selections of three letters which can be made from the letters of the word PARALLELOGRAM.
	www.brainmass.com /homework-help/math/other/5824 (264 words)

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