4.1 Organized Counting

	Date/Time	Made By	Edit Note	Type	Scope
	Jun 10 2007, 6:43 PM EDT	tofu-la		edit	9 words added 2 words deleted
Change: .By adding the two possible ways, we can figure out the total number of ways for Jim to roll a 1 or a number higher than 4. Jim can roll the number he wants in 3 ways. TreeFirst tree diagram provided by <http://www.gliffy.com/>Second tree diagram by tofu-la View changes from previous version. (Word count: 774)
	Jun 10 2007, 6:32 PM EDT	tofu-la	corrected spelling error	edit	3 words added
Change: X Total # of drinks X Total # of desserts = Total # of possibilitiesFundamental or Multiplicative Counting Principle A SIMPLER METHOD ¤ If a task is made up of stages with separate choices in each stage, the total number of ways of doing the task is m x View changes from previous version. (Word count: 767)
	Jun 10 2007, 6:29 PM EDT	tofu-la	new example added, moved words around to make understanding easier	edit	159 words added 42 words deleted 3 images added 2 images deleted
Change: a sandwich, drink and dessert. The cafeteria sells BLT, Tuna, and Club sandwiches. For drinks they offer, orange juice, iced tea, apple juice and coke, and as for dessert, they sell brownies and cookies. How many different combinations of prizesandwich, packagesdrink and dessert can one person make? Number View changes from previous version. (Word count: 765)
	Dec 27 2006, 2:42 PM EST	aneta29		edit	1 word added 1 word deleted
Change: nubernumber of ways of doing the task is m x n x p..., where 'm' is the number of choices for the 1st stage, 'n' is the number of choices for the 2nd stage and so on. The Fundamental Counting Principle View changes from previous version. (Word count: 650)
	Nov 19 2006, 1:32 PM EST	Anika		edit	7 words added 9 words deleted
Change: 6 561478 0002969Therefore, there are 6 561478 0002969 phone numbers that do not have two of the same numbers next to each other. (c) How many phone numbers do not repeat the same number at all? 9 9 8 7 6 5 4 = View changes from previous version. (Word count: 650)
	Nov 10 2006, 4:56 PM EST	aneta29		edit	25 words added 5 words deleted
Change: the phone number can NOT begin with 0; however the other numbers in the phone number can include 0. 9 9 10 9 10 9 10 = 6 561 000Therefore, there are 6 561 000 phone numbers that do View changes from previous version. (Word count: 652)
	Nov 10 2006, 4:44 PM EST	aneta29		edit	5 words added 5 words deleted
Change: 109 9 10 9 10 9 10 = 76 290561 000Therefore, there are 76 290561 000 phone numbers that do not have two of the same numbers next to each other. (c) How many phone numbers do not repeat the same number at all? View changes from previous version. (Word count: 632)
	Nov 3 2006, 8:58 PM EST	aneta29		edit	2 words added 2 words deleted
Change: The(The Additive Counting Priciple is applied in the following exampleexample.)Example 3: Jim is playing Monopoly with his friends. They are playing with one die. Jim, during his turn, either View changes from previous version. (Word count: 632)
	Nov 3 2006, 6:53 PM EST	Anika		edit	58 words added 4 words deleted
Change: , meaning they cannot be performed at the same time, then there are m + n ways of doing the task.The Additive Counting Priciple is applied in the following exampleExample 3: Jim is playing Monopoly with his friends. They are View changes from previous version. (Word count: 632)
	Nov 3 2006, 6:11 PM EST	aneta29		edit
Change: There were only format changes (bold, italics, etc.) in this version. See this version for details. (Word count: 580)
	Nov 3 2006, 6:11 PM EST	aneta29		edit	2 words added 2 words deleted
Change: Tree DiagramExample 1: Tree DiagramA radio station announces that they are giving away a prize package to the first caller. The package involves 1 movie, 1 View changes from previous version. (Word count: 580)
	Nov 3 2006, 6:05 PM EST	aneta29		edit
Change: There were only format changes (bold, italics, etc.) in this version. See this version for details. (Word count: 580)
	Nov 3 2006, 5:59 PM EST	aneta29		edit	4 words added 1 word deleted
Change: tasks are mutually exclusive.By adding the two possible ways, we can figure out the total number of ways for Jim to roll a 1 or a number higher than 4. Jim can roll the number he wants in 3 ways. References Tree diagram provided by >http://www.gliffy.com/< View changes from previous version. (Word count: 580)
	Nov 3 2006, 5:56 PM EST	aneta29		edit
Change: There were only format changes (bold, italics, etc.) in this version. See this version for details. (Word count: 577)
	Nov 3 2006, 5:55 PM EST	aneta29		edit
Change: There were only format changes (bold, italics, etc.) in this version. See this version for details. (Word count: 577)
	Nov 3 2006, 5:12 PM EST	aneta29		edit	2 words added 2 words deleted
Change: Example 3: Additive Counting PrincipleExample 3: Jim is playing Monopoly with his friends. They are playing with one die. Jim, during his turn, either wants to roll a View changes from previous version. (Word count: 577)
	Nov 3 2006, 5:09 PM EST	aneta29		edit	39 words added 1 word deleted
Change: not have two of the same numbers next to each other.(c) How many phone numbers do not repeat the same number at all? 10 9 8 7 6 5 4 = 604 800 Therefore, there are 604 800 phone numbers that do not repeat the same number at all. View changes from previous version. (Word count: 577)
	Nov 3 2006, 5:02 PM EST	aneta29		edit	1 word added 1 word deleted
Change: 0)0 9 10 10 10 10 10 10 = 9 x 10 x 10 x 10 x 10 x 10 x 10 = 9 000 000 Therefore, there are 9 000 000 possible phone numbers.(b) How many possible phone numbers are View changes from previous version. (Word count: 539)
	Nov 3 2006, 5:00 PM EST	aneta29		edit	17 words added 11 words deleted
Change: Therefore, there are 9 000 000 possible phone numbers.(b) How many possible phone numbers are there that do not have two of the same number next to each other? 10 9 10 9 10 9 10 = 7 290 000(c) How many phone numbers View changes from previous version. (Word count: 539)
	Nov 3 2006, 4:54 PM EST	aneta29		edit	26 words added 8 words deleted
Change: (The Fundaments Counting Principle is applied in the following example.) Example 2: PhoneTelephone numbers in Canada used to be 7 digits,digits and they did not include an area code. (a) How many 7 digit phone numbers are there? Task?Task: writing down 7 numbers Number of stages?stages: View changes from previous version. (Word count: 533)

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