Combination

“Combination” is popularly known as a branch of “Mathematics”. It can be used for creating a new set of arrangements of objects by following a set of given rules. In this context, the best arrangement can be found from the given objects under different types of circumstances. There are two types of “Enumerations” in “Combination”, the “Counting Method” and the “Graph Theory”. In “Combination” the order of the group of objects doesn’t matter. The study of “Combination” is dependent on “Permutation” while studying “Mathematics”. This branch of study deals with calculations based on “Probability”.

Discussion

Evolution of Combination

The concept of “Combination” can be dated back to 2800 B.C. It is noted that the early stages of “Magic Squares” were used by the Chinese. However, the “Probability Theory” was brought up by “French Mathematicians” named “Blaise Pascal” and “Pierre de Fermat” in the “17 th century”. They developed it by considering the ratio of desired subsets of numbers to the possible number of available subsets. “Bhaskara Acharya” the “12 th century” Indian “Mathematician” has included the description of “Integer Coefficients” of “(a+b)n” which is also known as the “Binomial Coefficients”. Studying the “Binomial Coefficients” relied highly on “Combinations”.

Difference between “Permutation” and “Combination”

“Permutation” deals with the different ways of arrangement of different objects. The order of the objects is kept into consideration in this particular case. So it can be stated that “Permutation” deals with the arrangement of different objects in their “Sequential” order. The things that have to be kept in mind while doing “Permutation” are “Arrangement”, “Placement” and “Order” of the objects. The formula based on which the evaluation of “Permutation” is done is indicated by: 

“nPr = n! / [(n – r)!]”. The examples that can be considered for “Permutation” are: “Alphabets”, “Numbers”.

On the other hand “Combination” deals with the different ways of selecting objects. In this case, the order of the objects is not taken into consideration. The things that have to be kept in mind evaluating “Combination” are: “Selection”, “Grouping” and “Choosing” of the given objects. The formula based on which the evaluation of “Combination” is done is indicated by: 

“nCr = n!/[r!(n-r)!] = nPr/r!”. The examples that can be considered for “Combination” are “Selecting Team Members” and others.

“Combinations” can be used in different areas of “Mathematics”, “Finance” and other disciplines. The permutation is considered as nothing but the single combination based on pair-values with sets of the selected features.

Example of Combination

Consider the researcher has three mates, Arpit, Rajul, and Surbhi. The researcher wants two of his pals to go shopping. He is unable to decide which of the two friends is to be taken along. An idea strikes the mind of the researcher that he will write the name of every friend individually on a piece of paper and randomly pick any two. Then the possible combination of friends can be:

• Arpit and Rajul

• Rajul and Surbhi

• Arpit and Surbhi

Therefore, it is visible that there are three probable ways of selecting any two friends out of three friends.

Formula for finding Combination

“nCr = n!/[r!(n-r)!] = nPr/r!”

“nCr” stands for the “Number of Combinators”, “n” stands for the “number of objects present in the set” and “r” stands for the “number of choosing objects from the given set”.

Types of Combination

It is noted that there are three different types of “Combinations”. One type of “Combination” deals with two types of “Elements”. Then there is another type of combination that deals with two types of “Compounds”. And another type of combination deals with “Element” and “Compound”.

Application of Combination

“Combination” can be used in the “Financial Sector” and various other disciplines. Most widely used is “Arrangement”. The arrangement of “People”, “Books”, “Letters”, “Alphabets” and many others. It is also applicable for the selection of different “Subjects”, “Team”, “Menu”, “Clothes” and others. It can also be used in real-life situations such as “Cryptography”.

Importance of Combination

“Combination” is the branch of the study of “Mathematics” that deals with the “Number of Possible Arrangements” in a number of given objects. The order of the selected objects does not matter while evaluating “Combination”. In this case, the given objects can be selected randomly in any order. It is a “Mathematical Technique” that is used for calculations in different sectors such as “Finance” and other disciplines.

Conclusion

Throughout the paper, the researcher has illustrated “Combination” in “Mathematics”. The researcher has discussed the evolution of “Combination”, the difference between “Permutation” and “Combination”. The formula of “Combination” has been mentioned and an example has been used to explain it thoroughly. The practical and theoretical uses of “Combination” have been discussed. From this paper, it can be deciphered that “Combination” is majorly used for “Arrangement” purposes. Arrangements of the people, books, menu, and many others, “Combination” takes into consideration dealing with the selection of different objects. In this context for evaluation of “Combination”, the order of the objects is not taken into consideration. “Selection”, “Grouping” and “Choosing” have to be kept in mind while evaluating it.