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Permutations and Combinations - Coggle Diagram
Permutations and Combinations
Perms and Coms with Restrictions
When perms has restrictions, the factorial equation is times-ed by the factorial equation of the other option. An example of this would be (₃P₃)(₈P₈). If you use the counting system, the restrictions will apply to the slots corresponding to the question asked. An example of this would be 1x5x4x3x2x1 = 120. for grouping, factorials are the most common used. The amount left from minusing the group is times-ed by the number of ways to arrange the group. an example of this would be 4! x 2! = 48.
When combs has restrictions, the factorial equation is either times-ed by one or the factorial equation is equal to one times the factorial equation that is left. An example of this would be (₁C₁)(₄C₂).
Combinations
Factorial equation
The factorial equation ₀C₁ is one of the only methods we use the most for combs. The 0 represents the amount of different options available. The C represents that the equation is a combination. The 1 represents the amount of options that must be chosen.
The factorial equation can also be represented as 0! / (0-1)! 1!.
Permutations
Counting system
The counting systems takes the factorial equation (₀P₁) and uses it to make a base. The amount of multiple slots available in the counting system is based on the 1. The 0 represents the amount of different options available.
Factorial
A factorial is basically the factorial equation except it is simplified and both values are the same. an example of this would be 5! = ₅P₅ as they both will equal 120.
Tree diagram
A tree diagram is a confusing and time consuming method for solving permutations. Tree diagrams map out every possible outcome within the questions context.
Factorial equation
The factorial equation ₀P₁ is a more complex version of a factorial. The 0 represents the amount of different options available. The P represents that the equation is a permutation. The 1 represents the amount of slots available.
The factorial equation can also be represented as 0! / (0-1)!.
Perms with Duplicates and combs with chose and arrange
When there are duplicates with perms, the factorial for the equation is taken and divided by the amount of repeats there are. An example of this would be 5!/2!
When there is a chose and arrange with combs, the factorial equation is times-ed with a factorial of how much the chosen group is. An example of this would be (₆C₂)(₄C₂) x 4!.