Counting techniques

Counting techniques

1. Multiplication

   • The multiplication rule is a way to find the probability of two events happening at the same time
     • The general multiplication rule formula is: P(A ∩ B) = P(A) P(B|A) and the specific multiplication rule is P(A and B) = P(A) * P(B).
   • https://www.statisticshowto.com/multiplication-rule-probability/#:~:text=The%20multiplication%20rule%20is%20a,of%20the%20AP%20Statistics%20formulas).&text=The%20general%20multiplication%20rule%20formula,)%20*%20P(B).

2. Permutation

   • Permutation is used for lists (order matters) and Combination for groups (order doesn't matter). Are all possible ways of arranging the elements of a set.
     • The formula for a permutation is: P(n,r) = n! / (n-r)!

3. Combination

   • A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter
     • The combinations formula is: nCr = n! / ((n – r)! r!) n = the number of items.
   • https://corporatefinanceinstitute.com/resources/knowledge/other/combination/#:~:text=A%20combination%20is%20a%20mathematical,the%20selection%20does%20not%20matter.&text=Combinations%20are%20studied%20in%20combinatorics,disciplines%2C%20including%20mathematics%20and%20finance.

4. https://towardsdatascience.com/difference-between-permutation-and-combination-9e12b6763ee1

5. Conclusion: Counting techniques are important and useful because they help to have mathematical tools for counting the size of the sample space and event space