# Permutations And Combinations class 11 Notes Mathematics

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## Permutations And Combinations class 11 Notes Mathematics

Download CBSE class 11th revision notes for Chapter 7 Permutations And Combinations class 11 Notes Mathematics in PDF format for free. Download revision notes for Permutations And Combinations class 11 Notes Mathematics and score high in exams. These are the Permutations And Combinations class 11 Notes Mathematics prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the best tips recommended by teachers during exam days.

CBSE Class 11 Mathematics
Revision Notes
Chapter-7
Permutations and Combinations

1. Fundamental Principle of Counting
2. Permutations
3. Combinations

Fundamental Principle of Counting

• Addition Law: If there are two operations such that such that they can be performed independently in $m$ and $n$ ways respectively, then either of the two operations can be performed in $(m+n)$ ways.
• Multiplication: If one operation can be performed in $m$ ways and if corresponding to each of the $m$ ways of performing this operation, there are $n$ ways of performing a second operation, then the number of ways of performing two operations together in $m \times n$.
• Factorial Notation: The continued product of first $n$ natural numbers is called the ‘$n$ factorial’ and is denoted by $n!$.
• $0! = 1$
• Permutations: The number of permutations of n different things taken r at a time, where repetition is not allowed, is denoted by $^{n}{{P}_{r}}$ and is given by $^{n}{{P}_{r}}=\frac{n!}{(n-r)!}$

$\text{where }0\text{ }\le \text{ r }\le \text{ n}.$

$\text{n}!\text{ }=\text{ 1 }\times \text{ 2 }\times \text{ 3 }\times \text{ }...\times \text{n}$

${\text{n}}!{\text{ }} = \;{\text{n }} \times {\text{ }}\left( {{\text{n }}-{\text{ 1}}} \right){\text{ }}!$

• The number of permutations of n different things, taken r at a time, where repeatition is allowed, is ${{n}^{r}}$.
• The number of permutations of  n objects taken all at a time, where  ${{\text{p}}_{1}}$ object are of first kind, ${{\text{p}}_{2}}^{{}}$ objects are of the second kind, …,${{\text{p}}_{k}}$ objects are of the ${{\text{k}}^{th}}$ kind and rest, if any, are all different is $\frac{n!}{{{p}_{1}}!{{p}_{2}}!..{{p}_{k}}!}.$

Combinations:

• The number of combinations of n different things taken r at a time, denoted by $^{n}{{C}_{r}}$ is given by $^{n}{{C}_{r}}=\frac{n!}{r!(n-r)!},o\le r\le n.$
• $^n{{\rm{C}}_0} = 1$
• $^n{{\rm{C}}_n} = 1$
• $^n{{\rm{C}}_r}{ = ^n}{{\rm{C}}_{n - r}}$
• $^n{{\rm{C}}_r}{ + ^n}{{\rm{C}}_{r - 1}}{ = ^{n + 1}}{{\rm{C}}_r}$
• $^n{{\rm{C}}_r} = {n \over r}{.^{n - 1}}{{\rm{C}}_{r - 1}}$
• $n{.^{n - 1}}{{\rm{C}}_{r - 1}} = {\left( {n - r + 1} \right)^n}{{\rm{C}}_{r - 1}}$
• Division into Groups: The number of ways $m+n$ things can be divided into two groups containing $m$ and $n$ things respectively = $^{m + n}{{\rm{C}}_m} = {{\left( {m + n} \right)!} \over {m!.n!}}$

## The Permutations And Combinations class 11 Notes

• CBSE Revision notes for Class 11 Mathematics PDF
• CBSE Revision notes Class 11 Mathematics – CBSE
• CBSE Revisions notes and Key Points Class 11 Mathematics
• Summary of the NCERT books all chapters in Mathematics class 11
• Short notes for CBSE class 11th Mathematics
• Key notes and chapter summary of Mathematics class 11
• Quick revision notes for CBSE exams

## CBSE Class-11 Revision Notes and Key Points

Permutations And Combinations class 11 Notes Mathematics. CBSE quick revision note for class-11 Mathematics, Physics, Chemistry, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

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