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Quarterly Exam Reviewer - Permutation and Combination - Mutually Exclussive
Cardinality
It is the number of elements in a given set.
Tree Diagram
A device used to list all possibilities of a sequence of events in a systematic way.
n1 x n2 x n3 x … ways
The fundamental counting principle states that if one event can occur in n1 ways, a second event can occur in n2 ways, and a third event can occur in n3 ways, and so on, then these events can occur in ______________
Permutation
The arrangement of objects in which order is important
n!
If n is equal to r, then nPr=___
1
If r is equal to 0, then nPr=___
n
If r is equal to 1, then nPr=___
nPr = n! / (n - r)!
The formula for permutation
Distinguishable Permutation
The arrangement of objects with identical objects.
P = n! divided by n1!n2!n3!…nk!
Formula for distiguishable objects
Circular Permutation
The arrangement of objects in a circular manner
P= n!/n or P= (n - 1)!
Formula for circular permutation
P= (n - 1)! divided by 2
Formula for circular permutation (key ring)
P= [(n - 1) - 1]! 2!
Formula for circular permutation if 2 wanted to be together
(n - 1)!
minus
[(n - 1) - 1]! 2!
Formula for circular permutation if 2 does not want to be together
Combination
An arrangement of n objects with no repetitions and the order is NOT important
nCr= nPr divided by r!
or
nCr= n! divided by (n - r)! r!
Formula for combination
Mutually Exclusive Events
This is when the events are impossible to happen at the same time
P(A U B)= P(A) +P(B)
Mutually Exclusive Events Formula
Non-Mutually Exclusive Events
This is when the events are can happen at the same time
P(A U B)= P(A) +P(B) - P(A ∩ B)
Non-Mutually Exclusive Events Formula
Dependent Events
The result of one event can affect the result on another event
Independent
The result of one event does NOT affect the result on another event
P(A and B)= P(A) x P(B)
Independent Formula
P(A and B)= P(A) x P(B/A)
Dependent Formula
Sample Space
The set of elements
1
In a dependent event P(A and B)= P(A) x P(B after A is taken)
The sample events in P(B/A) will be reduced by ___
