Summary of multiplication rules and probability basic theory

Multiplication Rules |
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Factorial0!=1 1!=1 2!=2∙1=2 3!=3∙2∙1=6 4!=4∙3∙2∙1=24 |

Basic Rules of Multiplication1. 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 =n^{r} |

Permutation Formulas1. The numbers of ways to arrange r different elements taken from the available n elements2. 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 k^{th} type |

Circular PermutationsThe number of different formation of n elements arranged circularly =(n-1)! |

CombinationsThe number of ways to collection of r elements taken from n elements which is given by |

Probability or Chance |
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In an experiment: The results of all of the experiment =NSuppose A is an event which is formed from the k results of these experiments, then the probability of the event AExpectation 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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