Combinatorics - Revision history

SamHB: Should be in main mathematics category also. See talk.

2018-09-22T02:27:37Z

Should be in main mathematics category also. See talk.

Quidam65: move to sub-category as requested by administrators due to Mathematics category becoming too large

2018-09-22T00:44:06Z

move to sub-category as requested by administrators due to Mathematics category becoming too large

FredericBernard: Wikify

2017-09-12T14:08:43Z

Wikify

GregG: /* Combinations */ add the binomial formula, a canonical application of binomial coefficients

2017-01-07T04:24:10Z

Combinations: add the binomial formula, a canonical application of binomial coefficients

DavidB4-bot: clean up & uniformity

2016-07-13T06:32:47Z

clean up & uniformity

ChrisGT90: Added references section

2010-06-03T01:53:21Z

Added references section

DiEb at 12:37, August 8, 2008

2008-08-08T12:37:14Z

HelpJazz: Undo revision 417372 by Special:Contributions/HelpJazz (User talk:HelpJazz) let's see if I can't get this to work

2008-04-06T22:19:57Z

Undo revision 417372 by Special:Contributions/HelpJazz (User talk:HelpJazz) let's see if I can't get this to work

HelpJazz: /* Combinations */ uh this could be a problem... "choose" won't parse

2008-03-30T19:29:15Z

Combinations: uh this could be a problem... "choose" won't parse

HelpJazz: more

2008-03-30T19:27:54Z

← Older revision		Revision as of 02:27, September 22, 2018
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	[[Category:Probability and Statistics]]		[[Category:Probability and Statistics]]
		+	[[Category:Mathematics]]

← Older revision		Revision as of 00:44, September 22, 2018
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	<references/>		<references/>

−	[[Category:~~Mathematics~~]]	+	[[Category:Probability and Statistics]]

@@ Line 22: / Line 22: @@
 For example, take a race which has 10 competitors. There are 10 choose 3 different combinations of medal winners (that is, racers who get either 1st, 2nd, or 3rd place), which is a total of 10! / (10 - 3)! • 3! = 10! / 7! • 3! = 120 different combinations.
-The numbers <math>\begin{pmatrix} n \\ r \end{pmatrix}</math> are also called binomial coefficients because of the expansion:
+The numbers <math>\begin{pmatrix} n \\ r \end{pmatrix}</math> are also called binomial coefficients because of the [[binomial expansion]]:
 :<math>(x + y)^n = \sum_{r = 0}^n \begin{pmatrix} n \\ r \end{pmatrix} x^r y^{n-r}</math>

@@ Line 20: / Line 20: @@
 :<math>\begin{pmatrix} n \\ r \end{pmatrix} = \frac{n!}{(n-r)!r!}</math>
 For example, take a race which has 10 competitors. There are 10 choose 3 different combinations of medal winners (that is, racers who get either 1st, 2nd, or 3rd place), which is a total of 10! / (10 - 3)! • 3! = 10! / 7! • 3! = 120 different combinations.
 ==References==

@@ Line 13: / Line 13: @@
 :<math>\frac {n!}{n_1! n_2! \cdot \cdot \cdot n_r!}</math>, where ''n'' is the total number of objects, and ''n<sub>1</sub>'' through ''n<sub>r</sub>'' are the total number of each type of objects within the group.
-For example, the letters ''p'' and ''e'' in the word "pepper" are indistinguishable from one another. There are 6 total letters, which are comprised of 3 <i>p</i>'s, 2 <i>e</i>'s, and 1 ''r''. The total number of permutations would thus be 6! / (3 ! 2! 1!), or 60.
+For example, the letters ''p'' and ''e'' in the word "pepper" are indistinguishable from one another. There are 6 total letters, which are comprised of 3 ''p'''s, 2 ''e'''s, and 1 ''r''. The total number of permutations would thus be 6! / (3 ! 2! 1!), or 60.
 ===Combinations===
@@ Line 25: / Line 25: @@
 <references/>
-[[category: mathematics]]
+[[Category:Mathematics]]

← Older revision		Revision as of 01:53, June 3, 2010
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	For example, take a race which has 10 competitors. There are 10 choose 3 different combinations of medal winners (that is, racers who get either 1st, 2nd, or 3rd place), which is a total of 10! / (10 - 3)! • 3! = 10! / 7! • 3! = 120 different combinations.		For example, take a race which has 10 competitors. There are 10 choose 3 different combinations of medal winners (that is, racers who get either 1st, 2nd, or 3rd place), which is a total of 10! / (10 - 3)! • 3! = 10! / 7! • 3! = 120 different combinations.
		+
		+	==References==
		+	<references/>

	[[category: mathematics]]		[[category: mathematics]]

← Older revision		Revision as of 12:37, August 8, 2008
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−	'''Combinatorics''' is a field of [[mathematics]] devoted to the study of counting ~~elemenents~~ in a set, and mathematical relations that describe their properties. This field is "[[discrete mathematics\|discrete]]", meaning it deals with non-[[continuous]] properties. Combinatorics is very useful in the field of discrete [[probability]] theory.	+	'''Combinatorics''' is a field of [[mathematics]] devoted to the study of counting elements in a set, and mathematical relations that describe their properties. This field is "[[discrete mathematics\|discrete]]", meaning it deals with non-[[continuous]] properties. Combinatorics is very useful in the field of discrete [[probability]] theory.

	==Combinatorial Functions==		==Combinatorial Functions==

← Older revision		Revision as of 22:19, April 6, 2008
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	For example, the letters ''p'' and ''e'' in the word "pepper" are indistinguishable from one another. There are 6 total letters, which are comprised of 3 <i>p</i>'s, 2 <i>e</i>'s, and 1 ''r''. The total number of permutations would thus be 6! / (3 ! 2! 1!), or 60.		For example, the letters ''p'' and ''e'' in the word "pepper" are indistinguishable from one another. There are 6 total letters, which are comprised of 3 <i>p</i>'s, 2 <i>e</i>'s, and 1 ''r''. The total number of permutations would thus be 6! / (3 ! 2! 1!), or 60.

		+	===Combinations===
		+	It is often useful to find out how many groups of ''r'' objects can be created out of a group of ''n'' objects. This can be calculated from a function called "choose" (read aloud as "n choose r"):
		+
		+	:<math>\begin{pmatrix} n \\ r \end{pmatrix} = \frac{n!}{(n-r)!r!}</math>
		+
		+	For example, take a race which has 10 competitors. There are 10 choose 3 different combinations of medal winners (that is, racers who get either 1st, 2nd, or 3rd place), which is a total of 10! / (10 - 3)! • 3! = 10! / 7! • 3! = 120 different combinations.

	[[category: mathematics]]		[[category: mathematics]]

← Older revision		Revision as of 19:29, March 30, 2008
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	For example, the letters ''p'' and ''e'' in the word "pepper" are indistinguishable from one another. There are 6 total letters, which are comprised of 3 <i>p</i>'s, 2 <i>e</i>'s, and 1 ''r''. The total number of permutations would thus be 6! / (3 ! 2! 1!), or 60.		For example, the letters ''p'' and ''e'' in the word "pepper" are indistinguishable from one another. There are 6 total letters, which are comprised of 3 <i>p</i>'s, 2 <i>e</i>'s, and 1 ''r''. The total number of permutations would thus be 6! / (3 ! 2! 1!), or 60.

−	~~===Combinations===~~
−	~~It is often useful to find out how many groups of ''r'' objects can be created out of a group of ''n'' objects. This can be calculated from a function called "choose" (read aloud as "n choose r"):~~
−
−	~~:<math> = \binom{n}{r} \frac{n!}{(n-r)!r!}</math>~~
−
−	For example, take a race which has 10 competitors. There are 10 choose 3 different combinations of medal winners (that is, racers who get either 1st, 2nd, or 3rd place), which is a total of 10! / (10 - 3)! • 3! = 10! / 7! • 3! = 120 different combinations.

	[[category: mathematics]]		[[category: mathematics]]

@@ Line 1: / Line 1: @@
-'''Combinatorics''' is a field of [[mathematics]] devoted to the study of counting elemenents in a set, and mathematical relations that describe their properties. This field is "[[Discrete mathematics|discrete]]", meaning it deals with non-[[continuous]] properties.
+'''Combinatorics''' is a field of [[mathematics]] devoted to the study of counting elemenents in a set, and mathematical relations that describe their properties. This field is "[[discrete mathematics|discrete]]", meaning it deals with non-[[continuous]] properties. Combinatorics is very useful in the field of discrete [[probability]] theory.
 ==Combinatorial Functions==
@@ Line 15: / Line 15: @@
 For example, the letters ''p'' and ''e'' in the word "pepper" are indistinguishable from one another. There are 6 total letters, which are comprised of 3 <i>p</i>'s, 2 <i>e</i>'s, and 1 ''r''. The total number of permutations would thus be 6! / (3 ! 2! 1!), or 60.
 [[category: mathematics]]