Difference between revisions of "Permutations And Combinations"

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*State that a combination is a selection and write the meaning of <math>{^{n}}C_{r}</math>
 
*State that a combination is a selection and write the meaning of <math>{^{n}}C_{r}</math>
 
*Distinguish between permutations and combinations;
 
*Distinguish between permutations and combinations;
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· derive <math>{^{n}}C_{r}</math>=<math>\frac{n!}{(n-r)!r!}</math>
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*Derive <math>{^{n}}C_{r}</math>=<math>\frac{n!}{(n-r)!r!}</math>
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and apply the result to solve problems;
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and apply the result to solve problems
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· derive the relation <math>{^{n}}P_{r}</math>=<math>{^{n}}C_{r}Xr!</math>
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*Derive the relation <math>{^{n}}P_{r}</math>=<math>{^{n}}C_{r} X r!</math>
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· verify that 4 and give its interpretation
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*Verify that <math>{^{n}}C_{n}</math>=<math>{^{n}}C_{n-r}</math> and give its interpretation
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· derive 5 and apply the result to solve problems.
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*Derive <math>{^{n}}C_{r} + ^{n}C_{n-r}</math>=<math>{^{n+1}}C_{r}</math> and apply the result to solve problems.
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−
 
 
−
 
 
−
 
 
−
 
 
−
 
 
−
 
 
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state that <math>{^{n}}P_{r}</math>=<math>\frac{n!}{(n-r)!}</math><br>and apply this to solve problems;
 
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*show that
 
−
#<math>{(n+1)^{n}}P_{n}</math>=<math>{^{n+1}}P_{n}</math><br>
 
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#<math>{^{n}}P_{r+1}</math>=<math>{(n-r)^{n}}P_{r}</math><br>
 
  
 
===Notes for teachers===
 
===Notes for teachers===

Revision as of 10:43, 7 August 2014

The Story of Mathematics

Philosophy of Mathematics

Teaching of Mathematics

Curriculum and Syllabus

Topics in School Mathematics

Textbooks

Question Bank

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Concept Map

Error: Mind Map file Permutation_and_Combinations.mm not found



Textbook

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

Additional Information

Useful websites

  1. mathsisfunPermutation and combination
  2. themathpagePermutation and combination

Useful video from khan academy and youtube

Reference Books

Teaching Outlines

Concept # 1 Fundamental Principle of Counting

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 to see the activity

  1. Activity No #2

Concept # 2 Factorial Notation

Learning objectives

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


Concept # 3 Permutations

Learning objectives

  • state that permutation is an arrangement and write the meaning of
  • state that =
    and apply this to solve problems;
  • show that
  1. =
  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

#Activity No # 1 Create-a-Bear Permutations click to see

#Activity No #2 Ice Cream Cone Permutations click to see

#Activity No #3 Arranging books click to see

Concept # 4 Arrangements with repetitions

Learning objectives

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 How to make Permutations


  1. Activity No #2


Concept # 5 Arrangements without repetitions

Learning objectives

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 How to make Permutations


  1. Activity No #2

Concept # 6 Combinations

Learning objectives

  • State that a combination is a selection and write the meaning of
  • Distinguish between permutations and combinations;
  • Derive =

and apply the result to solve problems

  • Derive the relation =
  • Verify that = and give its interpretation
  • Derive = 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 How to make Permutations


  1. Activity No #2

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. Class10_permutations_and_combinations_problems#Problem_2
  3. Class10_permutations_and_combinations_problems#Problem_3

Project Ideas

Math Fun

Usage

Create a new page and type {{subst:Math-Content}} to use this template

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