Permutations And Combinations

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= Concept Map =

= Textbook = To add textbook links, please follow these instructions to: ([ Click to create the subpage])

=Additional Information=

Useful websites
permutation and combination

Reference Books
= Teaching Outlines =

Notes for teachers
These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.

Activities
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 * 1) Activity No #2

Notes for teachers
These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.

Activities

 * 1) Activity No #1
 * 2) Activity No #2

=Assessment activities for CCE=

= Hints for difficult problems = 2) Triangles can be drawn through 8 points on a circle
 * 1)  How many 	1) lines`

Interpetation: drawing lines and triangle using the 8 points which are on a circumference of a  circle (irrespective of the position on circumference, may be equally spaced or not). And students should identify whether the problem is of arrengement or selection of objects.

Methods: 1) visual method		2) arithmetic way

Concepts: 1. circle 2. co-linear and non co-linear points 3. difference bet'n line, ray and segment 4. points require to draw a triangle 5. difference bet'n arrengements and selection for eg. If A and B are two objects then AB and BA are different arregements where as AB           and BA are both same when it comes to selection. 6. Expantion of Factorial

Solution:

1. for drawing lines we need atleast two points then selecting 2 points out of 8 given we have

= arrangements

n!		         =---	( students should know the formula) (n-r)! r!

8! 		         = ---	(substituting the values into the formula) (8-2)! 2!

8!		          = ---	(simplification) 6! 2!                            8*7*6*5*4*3*2*1	 	          =--	 		      6*5*4*3*2*1*2*1	 	          =4*7 		= 28

2. for drawing a triangle we need 3 non co-linear points then selecting 3 points out of 8 given we have = arrengements

n!	 	         =---		( students should know the formula) (n-r)! r!

8!	                = ---		(substituting the values into the formula) (8-3)! 3!

8!		          = ---		(simplification) 5! 3!                            8*7*6*5*4*3*2*1	 	          =--	 		      5*4*3*2*1*3*2*1	 	          =8*7

= 56

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