Permutations And Combinations

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= Concept Map = Flash

= Textbook =

=Additional Information=

Useful websites

 * 1) mathsisfunPermutation and combination
 * 2) themathpagePermutation and combination

Useful video from khan academy and youtube

Reference Books
NCERT text book on permutations and combinations click here

Gujarat state text book on permutations and combinations click here

= Teaching Outlines =

Learning objectives

 * 1) Students should be able to determine the number of outcomes in a problem
 * 2) Students should be able to apply the Fundamental principle of counting to find out the total number of outcomes in problem
 * 3) Students should be able to draw the tree diagram for the outcomes

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
Activity No # 1 Flipping a coin and a dice Click here

Activity No #2

Learning objectives

 * 1) Students should be able to use the factorial notation
 * 2) Students should be able to tell that n! is the product of first 'n' natural numbers
 * 3) Students should be able to know that if 'n' is a negative number or a decimal, n! is not defined
 * 4) Students should be able to know the value of 0!

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
Activity No # 1 For the activity to make students understand factorial notation please see the activity click here

Activity No # 2

Learning objectives

 * Sudents should be able to state that permutation is an arrangement and write the meaning of $${^{n}}P_{r}$$
 * Sudents should be able to state that $${^{n}}P_{r}$$=$$\frac{n!}{(n-r)!}$$ and apply this to solve problems
 * Sudents should be able to show that
 * 1) $${(n+1)^{n}}P_{n}$$=$${^{n+1}}P_{n}$$
 * 1) $${^{n}}P_{r+1}$$=$${(n-r)^{n}}P_{r}$$

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
Activity No # 1 Create-a-Bear Permutations click here

Activity No # 2 Ice Cream Cone Permutations click here

Activity No # 3 Arranging books click here

Learning objectives
and apply the result to solve problems
 * State that a combination is a selection and write the meaning of $${^{n}}C_{r}$$
 * Distinguish between permutations and combinations
 * Derive $${^{n}}C_{r}$$=$$\frac{n!}{(n-r)!r!}$$
 * Derive the relation $${^{n}}P_{r}$$=$${^{n}}C_{r} X r!$$
 * Verify that $${^{n}}C_{n}$$=$${^{n}}C_{n-r}$$ and give its interpretation
 * Derive $${^{n}}C_{r} + ^{n}C_{n-r}$$=$${^{n+1}}C_{r}$$ and apply the result to solve problems.

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
Activity No # 1 Be a Sport with Combinations click here

Activity No # 2 It's a Wrap with Combinations click here

Activity No # 3 Picking Books click here

=Assessment activities for CCE=

= Hints for difficult problems = 1.How many 3-digits numbers can be formed from the digits 0,1,2,3 and 4 without repetition?Solution 2.How many 4-digit numbers can be formed using the digits 1,2,3,7,8 and 9 (repetations not allowed)
 * 1) How many of these are less than 6000?
 * 2) How many of these are even?
 * 3) How many of these end with 7? Solution

3.How many
 * 1) lines
 * 2) Triangles can be drawn through 8 points on a circle Solution

= Project Ideas =

= Math Fun =

Usage

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