Permutations and combinations

Hello students, in this blog we are going to discuss the topic of permutations and combinations. These two topics are extensively used in mathematics.
Permutations: - The different arrangement of a given number of things by taking some or all at a time, are called the permutations. Let’s take a close look on the permutations.
All permutations made with the letter ‘a’, ‘b’, ‘c’ by taking two at a time are (ab, ba, ac, ca, bc, cb).
 All permutations made with the letter ‘a’, ‘b’, ‘c’ by taking all at a time are (abc, acb, bac, bca, cab, cba).
Combinations: As name suggest of the combination that it is concept in which every number of separate groups are made by the when we include few or all number of an object, then it is known as the combination.
Suppose we want to select two out of three boys A, B, C. Then possible selections are AB, BC and CA.
Note that AB and BA represent the same selections.
Formula for permutation and combination are:
For permutation: “P r = n (n - 1) (n - 2)……(n –r + 1) = n! / (n - r) !,
Example for this: 1. 6 p2 =(6 * 5) = 30.                  2. 7 P 3 = (7 * 6 * 5) = 210.
 For combination: “C r = n ! / (r !) (n - r) ! = (n - 1) (n - 2)……to r factors / r !,
Example. ¹¹ C ₄ = (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1) = 330, (know more about icse board papers, here)
So applying both the formulas we can solve any permutation and combination problems.
In the next session we will discuss about Types of events. 

Data representation methods

In statistics we have several methods of data representation that are used for represent the data in a specified manner that means once data is collected by the person or group of persons that is related with the specific experiment is then it will be presented in the way that user of data can understand it very easily and it is not used only for present scenario but also it will be used in future for making some decisions or for comparing the results of different years , so there are some well defined methods of data representation in statistics that helps the user of data to make efficient and effective decision very efficiently in very short span of time .These Data representation methods are as follows :
Data will be represented in the tabular form that will support to understand the data with its entire attributes.
For representing the data there one more technique that is known as graphs or pie charts that will help in understanding the way how data is changed in the particular environment or for specific experiment .
We can also draw some charts for representation of data.
The graphs are also categorized in some types that are line graph or histogram or bar graph or pyramids etc.
So for presenting the data there should some step that must be follow by the user for making the graphs or charts as: (know more about cbse sample papers for class 10, here)
First of all a suitable scale will be selected by the user.
After selection of scale follow all the design as index, directions and titles etc.
After it user select the appropriate way for representing the data that data will represent in two dimensional ways or in three dimensional ways.
In the next session we will discuss about conditional probability.