Permutations And Combinations

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

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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

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 here

Activity No #2

Concept # 2 Factorial Notation

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

Concept # 3 Permutations

Learning objectives

• State that permutation is an arrangement and write the meaning of ${^{n}}P_{r}$

• State that ${^{n}}P_{r}$=${\frac {n!}{(n-r)!}}$ and apply this to solve problems

• 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

Concept # 4 Combinations

Learning objectives

• State that a combination is a selection and write the meaning of ${^{n}}C_{r}$

• Distinguish between permutations and combinations

• Derive ${^{n}}C_{r}$=${\frac {n!}{(n-r)!r!}}$

and apply the result to solve problems

• Derive the relation ${^{n}}P_{r}$=${^{n}}C_{r}Xr!$

• 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

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

Math Fun

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