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Peiges

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	Page	Date/Time	Type	Scope
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 11:46 PM EDT	edit	1 word added
Change: can be summarized in this flow chart:This is a video of some of the permutations for a Rubik cube that lead to the solution of the cube.References: Mathematics of Data Management , Grade 12, (MDM4U). McGraw-Hill Ryersonhttp://www.youtube.com http://www.gliffy.comhttp://www.imeem.com View changes from previous version. (Word count: 418) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 11:42 PM EDT	edit	1 widget added
Change: There were only format changes (bold, italics, etc.) in this version. See this version for details. (Word count: 414) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 11:32 PM EDT	edit	13 words added 5 words deleted 1 image added 1 image deleted
Change: finding the number of permutations -can be summarized in this Flowflow Chart:chart:This is a video of some of the permutations for a Rubik cube that lead to the solution of the cube.References: Mathematics of Data Management , Grade 12, (MDM4U). McGraw-Hill Ryersonhttp://www.youtube.com http://www.gliffy.com View changes from previous version. (Word count: 414) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 10:05 PM EDT	edit	1 word added
Change: (ACP): (4.1 Organized Counting)Therefore, there are a total 210 distinct permutations. Process of finding permutations - Flowchart:This is a video of some rubik cube permutations that lead to the solution of the cube.References: Mathematics of Data Management , Grade 12, (MDM4U). McGraw-Hill Ryersonhttp://www.youtube.com http://www.gliffy.com View changes from previous version. (Word count: 393) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 9:59 PM EDT	edit	3 words added
Change: (ACP): (4.1 Organized Counting)Therefore, there are a total 210 distinct permutations. Process of finding permutations - Flowchart:This is a video of some rubik cube permutations that lead to the solution of the cube.References: Mathematics of Data Management , Grade 12, (MDM4U). McGraw-Hill Ryersonhttp://www.youtube.com View changes from previous version. (Word count: 389) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 9:56 PM EDT	edit	2 words added 1 word deleted
Change: Additive Counting Principle (ACP):Therefore, there are a total 210 distinct permutations. Process of finding permutations-permutations - Flowchart:This is a video of some rubik cube permutations that lead to the solution of the cube.References: Mathematics of Data Management , Grade 12, (MDM4U). McGraw-Hill Ryersonhttp://www.youtube.com View changes from previous version. (Word count: 385) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 9:56 PM EDT	edit	11 words added
Change: the Additive Counting Principle (ACP):Therefore, there are a total 210 distinct permutations. Process of finding permutations- Flowchart:This is a video of some rubik cube permutations that lead to the solution of the cube.References: Mathematics of Data Management , Grade 12, (MDM4U). McGraw-Hill Ryersonhttp://www.youtube.com View changes from previous version. (Word count: 385) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 9:51 PM EDT	edit	4 words added 1 word deleted
Change: First digit is 1 and last digit is 2.Now use the Additive Counting Principle (ACP):(ACP):Therefore, there are a total 210 distinct permutations. Process of finding permutations- Flowchart:This is a video of some rubik cube permutations that lead to the solution of the cube.References: View changes from previous version. (Word count: 371) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 9:49 PM EDT	edit	17 words added 23 words deleted 1 image added 1 widget added
Change: Total # of permutations = Case 1+ Case 2+ Case 3+ Case 4 = 30 + 60 + 60 + 60 = 210Therefore, there are a total 210 distinct permutations. Process of finding permutations- Flowchart:This is a video of some rubik cube permutations that View changes from previous version. (Word count: 370) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 9:39 PM EDT	edit	38 words added 2 words deleted 3 images added 3 images deleted
Change: last digit is 2.Now use the Additive Counting Principle (ACP): Total # of permutations = Case 1+ Case 2+ Case 3+ Case 4 = 30 + 60 + 60 + 60 = 210Therefore, there are a total 210 distinct permutations. Process of finding permutations- Flowchart: View changes from previous version. (Word count: 369) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 9:26 PM EDT	edit	2 words added 4 images added
Change: and last digit is 6. (1) (6) Case 2: First digit is 2 and last digit is 6.Case 3: First digit is 2 and last digit is 2.Case 4: First digit is 1 and last digit is 2. Process of finding permutations- Flowchart: View changes from previous version. (Word count: 340) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 9:08 PM EDT	edit	70 words added
Change: How many 7-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5, 5, 6? This questions involves cases:Case 1: First digit is 1 and last digit is 6. Case 2: First digit is 2 and last digit is 6.Case View changes from previous version. (Word count: 338) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 9:00 PM EDT	edit	18 words added 4 words deleted 1 image added 1 image deleted
Change: How many distinct permutations can be made from the name AJAY?The name Ajay,AJAY, has a total number of permutations of 4!.These are not distinct permutations, the permutations of the identical letters (elements), “a”,“A”, does not affect the total number of distinct permutations possible.Therefore, the View changes from previous version. (Word count: 265) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 8:50 PM EDT	edit	4 words added 3 words deleted 1 image added
Change: 1:1: theThe name Ajay, has a total number of permutations of 4!.These are not distinct permutations, the permutations of the identical letters (elements), “a”, does not affect the total number of distinct permutations possible.Therefore, the number of distinct permutations for Ajay does not equal 4! View changes from previous version. (Word count: 252) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 8:41 PM EDT	edit	77 words added 3 words deleted 2 images added 1 image deleted
Change: total number of permutations for the arrangement of the six balls is 6!, but these are not distinct permutations. The distinction between the three blue View changes from previous version. (Word count: 252) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 8:19 PM EDT	edit	1 image added
Change: There were only format changes (bold, italics, etc.) in this version. See this version for details. (Word count: 179) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 8:13 PM EDT	edit	74 words added
Change: These are not distinct permutations, the permutations of the identical letters (elements), “a”, does not affect the total number of distinct permutations possible.Therefore, the number of distinct permutations for Ajay does not equal 4!To Eliminate the non-distinct permutations, the total number View changes from previous version. (Word count: 179) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 8:09 PM EDT	edit	1 image added 1 image deleted
Change: There were only format changes (bold, italics, etc.) in this version. See this version for details. (Word count: 104) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 8:05 PM EDT	edit	6 words deleted 2 images added
Change: P(n,r) = n! (n-r)! Example: What is the total number of arrangements for the following six balls if only three balls must be used? These two types were demonstrated in the previous lesson. (4.2 Factorials and Permutations)c) Permutations involving some identical elements; n! a!b!c!... Example: What is View changes from previous version. (Word count: 104) View all updates.
	4.3 Permutations with Some Identical Elements	Apr 26 2007, 7:47 PM EDT	edit
Change: There were only format changes (bold, italics, etc.) in this version. See this version for details. (Word count: 114) View all updates.

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