SlideShare a Scribd company logo
1 of 20
Product rule
Generalized product rule:

If we have a procedure consisting of sequential tasks T1, T2, …, Tm that can be done in n1,
n2, …, nm ways, respectively, then there are n1 n2 … nm ways to carry out the procedure.
K+1

k
Example : In our 60-student class, at least 12 students will get
the same letter grade (A, B, C, D, or F).
Fundamental principle of counting -Discrete Mathematics

More Related Content

What's hot

Mathematical Induction
Mathematical InductionMathematical Induction
Mathematical Induction
Edelyn Cagas
 
Linear Systems Gauss Seidel
Linear Systems   Gauss SeidelLinear Systems   Gauss Seidel
Linear Systems Gauss Seidel
Eric Davishahl
 

What's hot (20)

Number theory
Number theoryNumber theory
Number theory
 
Binomial Coefficient
Binomial CoefficientBinomial Coefficient
Binomial Coefficient
 
5.1 greedy
5.1 greedy5.1 greedy
5.1 greedy
 
Mathematical Induction
Mathematical InductionMathematical Induction
Mathematical Induction
 
Language
LanguageLanguage
Language
 
Modular arithmetic
Modular arithmeticModular arithmetic
Modular arithmetic
 
Linear Systems Gauss Seidel
Linear Systems   Gauss SeidelLinear Systems   Gauss Seidel
Linear Systems Gauss Seidel
 
Context free grammar
Context free grammar Context free grammar
Context free grammar
 
Theory of Computation
Theory of ComputationTheory of Computation
Theory of Computation
 
BOOLEAN ALGEBRA.ppt
BOOLEAN ALGEBRA.pptBOOLEAN ALGEBRA.ppt
BOOLEAN ALGEBRA.ppt
 
Recurrence relations
Recurrence relationsRecurrence relations
Recurrence relations
 
Automata theory
Automata theoryAutomata theory
Automata theory
 
Intro automata theory
Intro automata theory Intro automata theory
Intro automata theory
 
Huffman coding
Huffman coding Huffman coding
Huffman coding
 
Differential equations of first order
Differential equations of first orderDifferential equations of first order
Differential equations of first order
 
Combinational circuits
Combinational circuitsCombinational circuits
Combinational circuits
 
Combinatorics
CombinatoricsCombinatorics
Combinatorics
 
Regular expressions
Regular expressionsRegular expressions
Regular expressions
 
Introduction to Graph Theory
Introduction to Graph TheoryIntroduction to Graph Theory
Introduction to Graph Theory
 
DIFFERENTIAL EQUATIONS
DIFFERENTIAL EQUATIONSDIFFERENTIAL EQUATIONS
DIFFERENTIAL EQUATIONS
 

Viewers also liked

Discrete-Chapter 06 Counting
Discrete-Chapter 06 CountingDiscrete-Chapter 06 Counting
Discrete-Chapter 06 Counting
Wongyos Keardsri
 
Intoduction to Network Security NS1
Intoduction to Network Security NS1Intoduction to Network Security NS1
Intoduction to Network Security NS1
koolkampus
 
Scalable Internet Servers and Load Balancing
Scalable Internet Servers and Load BalancingScalable Internet Servers and Load Balancing
Scalable Internet Servers and Load Balancing
Information Technology
 
Intelligence, spies & espionage
Intelligence, spies & espionageIntelligence, spies & espionage
Intelligence, spies & espionage
dgnadt
 
ICCV2009: MAP Inference in Discrete Models: Part 5
ICCV2009: MAP Inference in Discrete Models: Part 5ICCV2009: MAP Inference in Discrete Models: Part 5
ICCV2009: MAP Inference in Discrete Models: Part 5
zukun
 

Viewers also liked (20)

Counting, pigeonhole, permuntation, Permutations and Combination ,Binomial T...
Counting,  pigeonhole, permuntation, Permutations and Combination ,Binomial T...Counting,  pigeonhole, permuntation, Permutations and Combination ,Binomial T...
Counting, pigeonhole, permuntation, Permutations and Combination ,Binomial T...
 
Discrete-Chapter 06 Counting
Discrete-Chapter 06 CountingDiscrete-Chapter 06 Counting
Discrete-Chapter 06 Counting
 
Trends in spies
Trends in spiesTrends in spies
Trends in spies
 
Functional style programming
Functional style programmingFunctional style programming
Functional style programming
 
Functional programming with python
Functional programming with pythonFunctional programming with python
Functional programming with python
 
Android Application: Introduction
Android Application: IntroductionAndroid Application: Introduction
Android Application: Introduction
 
Carrick - Introduction to Physics & Electronics - Spring Review 2012
Carrick - Introduction to Physics & Electronics - Spring Review 2012Carrick - Introduction to Physics & Electronics - Spring Review 2012
Carrick - Introduction to Physics & Electronics - Spring Review 2012
 
CITY OF SPIES BY SORAYYA KHAN
CITY OF SPIES BY SORAYYA KHANCITY OF SPIES BY SORAYYA KHAN
CITY OF SPIES BY SORAYYA KHAN
 
What is Network Security?
What is Network Security?What is Network Security?
What is Network Security?
 
Intoduction to Network Security NS1
Intoduction to Network Security NS1Intoduction to Network Security NS1
Intoduction to Network Security NS1
 
Securing Windows web servers
Securing Windows web serversSecuring Windows web servers
Securing Windows web servers
 
Android UI
Android UIAndroid UI
Android UI
 
Scalable Internet Servers and Load Balancing
Scalable Internet Servers and Load BalancingScalable Internet Servers and Load Balancing
Scalable Internet Servers and Load Balancing
 
Noah Z - Spies
Noah Z - SpiesNoah Z - Spies
Noah Z - Spies
 
Intelligence, spies & espionage
Intelligence, spies & espionageIntelligence, spies & espionage
Intelligence, spies & espionage
 
ICCV2009: MAP Inference in Discrete Models: Part 5
ICCV2009: MAP Inference in Discrete Models: Part 5ICCV2009: MAP Inference in Discrete Models: Part 5
ICCV2009: MAP Inference in Discrete Models: Part 5
 
Serial Killers Presentation1
Serial Killers Presentation1Serial Killers Presentation1
Serial Killers Presentation1
 
SAN
SANSAN
SAN
 
Lec 03 set
Lec 03   setLec 03   set
Lec 03 set
 
SAN Review
SAN ReviewSAN Review
SAN Review
 

Recently uploaded

Cloud Frontiers: A Deep Dive into Serverless Spatial Data and FME
Cloud Frontiers:  A Deep Dive into Serverless Spatial Data and FMECloud Frontiers:  A Deep Dive into Serverless Spatial Data and FME
Cloud Frontiers: A Deep Dive into Serverless Spatial Data and FME
Safe Software
 
+971581248768>> SAFE AND ORIGINAL ABORTION PILLS FOR SALE IN DUBAI AND ABUDHA...
+971581248768>> SAFE AND ORIGINAL ABORTION PILLS FOR SALE IN DUBAI AND ABUDHA...+971581248768>> SAFE AND ORIGINAL ABORTION PILLS FOR SALE IN DUBAI AND ABUDHA...
+971581248768>> SAFE AND ORIGINAL ABORTION PILLS FOR SALE IN DUBAI AND ABUDHA...
?#DUbAI#??##{{(☎️+971_581248768%)**%*]'#abortion pills for sale in dubai@
 

Recently uploaded (20)

Axa Assurance Maroc - Insurer Innovation Award 2024
Axa Assurance Maroc - Insurer Innovation Award 2024Axa Assurance Maroc - Insurer Innovation Award 2024
Axa Assurance Maroc - Insurer Innovation Award 2024
 
Corporate and higher education May webinar.pptx
Corporate and higher education May webinar.pptxCorporate and higher education May webinar.pptx
Corporate and higher education May webinar.pptx
 
Biography Of Angeliki Cooney | Senior Vice President Life Sciences | Albany, ...
Biography Of Angeliki Cooney | Senior Vice President Life Sciences | Albany, ...Biography Of Angeliki Cooney | Senior Vice President Life Sciences | Albany, ...
Biography Of Angeliki Cooney | Senior Vice President Life Sciences | Albany, ...
 
ProductAnonymous-April2024-WinProductDiscovery-MelissaKlemke
ProductAnonymous-April2024-WinProductDiscovery-MelissaKlemkeProductAnonymous-April2024-WinProductDiscovery-MelissaKlemke
ProductAnonymous-April2024-WinProductDiscovery-MelissaKlemke
 
Artificial Intelligence Chap.5 : Uncertainty
Artificial Intelligence Chap.5 : UncertaintyArtificial Intelligence Chap.5 : Uncertainty
Artificial Intelligence Chap.5 : Uncertainty
 
Apidays New York 2024 - The Good, the Bad and the Governed by David O'Neill, ...
Apidays New York 2024 - The Good, the Bad and the Governed by David O'Neill, ...Apidays New York 2024 - The Good, the Bad and the Governed by David O'Neill, ...
Apidays New York 2024 - The Good, the Bad and the Governed by David O'Neill, ...
 
Boost Fertility New Invention Ups Success Rates.pdf
Boost Fertility New Invention Ups Success Rates.pdfBoost Fertility New Invention Ups Success Rates.pdf
Boost Fertility New Invention Ups Success Rates.pdf
 
Apidays New York 2024 - The value of a flexible API Management solution for O...
Apidays New York 2024 - The value of a flexible API Management solution for O...Apidays New York 2024 - The value of a flexible API Management solution for O...
Apidays New York 2024 - The value of a flexible API Management solution for O...
 
Web Form Automation for Bonterra Impact Management (fka Social Solutions Apri...
Web Form Automation for Bonterra Impact Management (fka Social Solutions Apri...Web Form Automation for Bonterra Impact Management (fka Social Solutions Apri...
Web Form Automation for Bonterra Impact Management (fka Social Solutions Apri...
 
2024: Domino Containers - The Next Step. News from the Domino Container commu...
2024: Domino Containers - The Next Step. News from the Domino Container commu...2024: Domino Containers - The Next Step. News from the Domino Container commu...
2024: Domino Containers - The Next Step. News from the Domino Container commu...
 
"I see eyes in my soup": How Delivery Hero implemented the safety system for ...
"I see eyes in my soup": How Delivery Hero implemented the safety system for ..."I see eyes in my soup": How Delivery Hero implemented the safety system for ...
"I see eyes in my soup": How Delivery Hero implemented the safety system for ...
 
Cloud Frontiers: A Deep Dive into Serverless Spatial Data and FME
Cloud Frontiers:  A Deep Dive into Serverless Spatial Data and FMECloud Frontiers:  A Deep Dive into Serverless Spatial Data and FME
Cloud Frontiers: A Deep Dive into Serverless Spatial Data and FME
 
[BuildWithAI] Introduction to Gemini.pdf
[BuildWithAI] Introduction to Gemini.pdf[BuildWithAI] Introduction to Gemini.pdf
[BuildWithAI] Introduction to Gemini.pdf
 
AWS Community Day CPH - Three problems of Terraform
AWS Community Day CPH - Three problems of TerraformAWS Community Day CPH - Three problems of Terraform
AWS Community Day CPH - Three problems of Terraform
 
MINDCTI Revenue Release Quarter One 2024
MINDCTI Revenue Release Quarter One 2024MINDCTI Revenue Release Quarter One 2024
MINDCTI Revenue Release Quarter One 2024
 
Exploring the Future Potential of AI-Enabled Smartphone Processors
Exploring the Future Potential of AI-Enabled Smartphone ProcessorsExploring the Future Potential of AI-Enabled Smartphone Processors
Exploring the Future Potential of AI-Enabled Smartphone Processors
 
+971581248768>> SAFE AND ORIGINAL ABORTION PILLS FOR SALE IN DUBAI AND ABUDHA...
+971581248768>> SAFE AND ORIGINAL ABORTION PILLS FOR SALE IN DUBAI AND ABUDHA...+971581248768>> SAFE AND ORIGINAL ABORTION PILLS FOR SALE IN DUBAI AND ABUDHA...
+971581248768>> SAFE AND ORIGINAL ABORTION PILLS FOR SALE IN DUBAI AND ABUDHA...
 
Polkadot JAM Slides - Token2049 - By Dr. Gavin Wood
Polkadot JAM Slides - Token2049 - By Dr. Gavin WoodPolkadot JAM Slides - Token2049 - By Dr. Gavin Wood
Polkadot JAM Slides - Token2049 - By Dr. Gavin Wood
 
FWD Group - Insurer Innovation Award 2024
FWD Group - Insurer Innovation Award 2024FWD Group - Insurer Innovation Award 2024
FWD Group - Insurer Innovation Award 2024
 
Strategize a Smooth Tenant-to-tenant Migration and Copilot Takeoff
Strategize a Smooth Tenant-to-tenant Migration and Copilot TakeoffStrategize a Smooth Tenant-to-tenant Migration and Copilot Takeoff
Strategize a Smooth Tenant-to-tenant Migration and Copilot Takeoff
 

Fundamental principle of counting -Discrete Mathematics

  • 1.
  • 2.
  • 3.
  • 5.
  • 6.
  • 7.
  • 8. Generalized product rule: If we have a procedure consisting of sequential tasks T1, T2, …, Tm that can be done in n1, n2, …, nm ways, respectively, then there are n1 n2 … nm ways to carry out the procedure.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17. K+1 k
  • 18.
  • 19. Example : In our 60-student class, at least 12 students will get the same letter grade (A, B, C, D, or F).