Examples
☼ Sample Space : A set representing all possible outcomes of a random experiment is called a sample space and it is denoted by S or U.
Each outcome is called a sample point. The number of sample points…
☼ Unbiased Experiment : If each outcome of the experiment is equally likely to occur, then the experiment is known as an unbiased experiment.
e.g. When we throw a coin, …
☼ Random Experiment ( or trial ) : An experiment which can result in anyone of the several possible outcomes is called a random experiment or a trial.
e.g. (i) Tossing of a coin is a rando…
(4) In how many ways 7 persons stand in a row, if three particular persons do not stand together ?
Soln. 7 persons can stand in a row in 7 ! = 5040 ways ––––––––– ( 1 )
Three particular person …
☼ COMBINATION : When we have to choose a certain number of objects from a given set of objects in such a way that the order of selection is not important, the selection is known as a combination. Consider the following example…
☼ Circular Permutation : The total number of circular permutations of n distinct objects taken all at a time =
☼ PERMUTATIONS : In the above example, 2 objects were selected from 3 objects in such a way that the order of the arrangements is important.
Now, if there were n = 10 objects and r = 3 objects were to be selected, then we …
☼ Definition of Fundamental principal of counting : If one operation can be performed in m ways and if corresponding to each of the m…
☼ Factorials : Permutation and Combination is a topic which requires use of the concept of factorials. A factorial is the number obtained by multiplying all the positive integers less than or equal to a given positive integer. T…