# Summary of Multiplication Rules and Probability Basic Theory

Summary of multiplication rules and probability basic theory

Multiplication Rules
Factorial
0!=1
1!=1
2!=2∙1=2
3!=3∙2∙1=6
4!=4∙3∙2∙1=24
Basic Rules of Multiplication
1. An event that can occur in n ways, followed by other events that can occur in m ways, then these two events can occur simultaneously in the (m×n) ways.
2. The number of ways to arrange r elements that are taken from the available n elements, where the elements is arranged can be repeated =nr
Permutation Formulas
1. The numbers of ways to arrange r different elements taken from the available n elements

2. Permutations with elements repetition. The number of ways to arrange n elements of which there are q elements of type I, r elements of type II. …, and s elements of kth type
Circular Permutations
The number of different formation of n elements arranged circularly =(n-1)!
Combinations
The number of ways to collection of r elements taken from n elements which is given by
Probability or Chance
In an experiment: The results of all of the experiment =N
Suppose A is an event which is formed from the k results of these experiments, then the probability of the event A

Expectation frequency = probability of events × the number of experiments.Relation Of probability of event(s) and probability of the complementary events.
P(A)=1-P(Ᾱ)→P(Ᾱ)=1-P(A)
P(Ᾱ)=P(S)-P(A)

Suppose S states the sample space.
P(A∪B)=P(A)+P(B)-P(A∩B)

Conditional probability
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