MATH

• Distinguishable permutation is the arrangement of objects with identical objects.
• The formula for distinguishable permutation is n!/n1!n2!n3!....nk!
• Permutation is an arrangement of objects in which order is important.
• Permutation of n objects taken r at a time is nPr=n!/(n-r)!
• Permutation of n objects taken all at a time is nPn=n!
• Circular permutation is the different possible arrangements of objects in a circular manner.
• The numbers of Permutations, P, of n objects around a circle is given by Pn = (n-1)!
• The number of permutation of n different things around a key ring and the like is Pn=(n-1)!/2
• Combination is the arrangement of n objects in which order is not important.
• The formula for combination is nCr=n!/(n-r)!r!
• In probability, an experiment is process of repeating an activity whose outcomes are limited to well-defined choices.
• The set of well-defined possible outcomes or choices is statistical experiment is called a sample space.
• Experimental probability is found by repeating an experiment and observing the outcomes.
• The formula for experimental probability is P(event)=number of times occured/total number of trials
• Theoretical Probability of an event is the number of ways the event can occur (favorable outcomes) divided by the number of total outcpmes.
• The formula for theoretical probability is P(event)=number of favorable outcomes/number of total outcomes
• Two events are mutually exclusive if both events can not occur at the same time. These events have no common elements.
• Mutually Exclusive events are also called disjoint events.
• Not Mutually exclusive events are also called inclusive events.
• Two events are not mutually exclusive if both events can occur at the same time. These events have common elements.
• Formula for Mutually Exclusive events is P(A U B) = P(A) + P(B)
• Formula for Not Mutually Exclusive events is P(A U B) = P(A) + P(B) - P(A ∩ B)
• Compound probability - refers to the probability of two or more simple events occurring at the same time.
• Independent events - probability A does not affect the probability B
• The formula for independent event is P(A and B) = P(A ∩ B) = P(A) * P(B)
• Dependent events - probability A affects Probability B
• Formula for dependent events is P(A and B) = P(A ∩ B) = P(A) * P(B/A)