Counting Principles

Fundamental Counting Principle

Types of Problems:

  • Be able to state the Fundamental Counting Principle and be able to give an example to help support the Fundamental Counting Principle
  • Use the Fundamental Counting Principle to determine sample size, sample space, and probabilities related to sample space​

Notes & Handouts

Practice 

Video and other resources

Digital Resources

Permutation of n elements
​n!

Types of Problems:

  • Be able to determine the number of ways to select or arrange n items ​
  • Be able to use factorials in the determination of sample size and sample space
  • Be able to use permutation to determine sample size, sample space, and probabilities
  • Be able to distinguish the difference between n! and nPr

Notes & Handouts

Practice

​Video and other resources

​Digital Resources

Permutations of n elements taken r at a time
​nPr

​Types of Problems:

  • Be able to state the formula for nPr in terms of n and r​
  • Be able to use factorials and properties of factorials to determine the number of permutations given n and r are known 
  • Be able to distinguish similarities and differences between combination or nCr, and permutation or nPr

​Practice

​Video and other resources

​Notes & Handouts

​​Digital Resources

Distinguishable Permutations

​Types of Problems:

  • Acknowledge the impact of repetition in sample space on the number of possible permutations ​
  • Be able to use a provided formula that uses multiple variables and factorial mathematics to determine the number of distinguishable permutations and know when it was when appropriate to use same formula

​Practice

​Video and other resources

​Notes & Handouts

​Digital Resources

Combinations of n elements taken r at a time
​nCr

​​Types of Problems:

  • Be able to state the formula for nCr in terms of n and r​
  • Be able to use factorials and properties of factorials to determine the number of combination given n and r are known 
  • Be able to distinguish similarities and differences between combination or nCr, and permutation or nPr​
  • Be able to connect the formula for nPr and nCr
  • Be able to to connect nCr to Pascal's Triangle

​​Notes & Handouts

​​Practice

​Video and other resources

​Digital Resources

Pascal's Triangle

​​Types of Problems:

  • Be able to produce n rows of Pascal's Triangle​
  • Be able to use Pascal's Triangle to quickly determine sample size and related probabilities 

​​Practice

​Video and other resources

​​Notes & Handouts

Digital Resources

Binomial Expansion of (a+b)^n

​​Types of Problems:

  • Be able to expand binomials raised to a power of n (with n being positive integer)​
  • Be able to connect Pascal's triangle to the expansion of a binomial raised to a power of n

​​Practice

​​Video and other resources

​​Notes & Handouts

Digital Resources

Additional Resources