## Introduction

The concept of selection and arrangement of things is very important in business mathematics. Often we are presented with certain problems, the solution of which requires the concept of permutation and combination. In simple terms, permutation and combination can be defined as some particular ways of representing a group of objects through selecting the data in a particular manner from the overall subset. When the selection of an object or data is done from a particular group then it is called a permutation. On the other hand, the order in which the representation is done is known as combinations. Both these concepts are vital in business mathematics.

## The basic concept of permutation and combination

In business mathematics, the concept of permutation is defined as the act of arrangement of every member of a particular set into some order or sequence.

On the other hand, the combination is defined as a method of choosing items from a particular collection so that the order of choice does not matter.

## Basic concepts of permutation and combination in BCA

Bachelors in Computer Application is the full form of BCA. It is an undergraduate degree program with a duration of 3 years. It helps students in focusing on knowledge concerning computers. However, some concepts of business mathematics are also studied in this course. Permutation and combination is one such important concept that is studied in the second year of BCA.

In BCA, the basic concepts of permutation and combination are the same as that in overall mathematics. The definitions are quite similar. There are several formulas involved within the combination and permutation concepts. The key formulas that are generally used have been mentioned in the following. Firstly there is the permutation formula. A permutation is defined as a particular selection of r items within a set of n items without replacement. Here the order of the items matter.

Next, there is the combination formula. A combination is defined as the selection of r items within a set of n items without replacement. Here the order of the items does not matter.

## Basic concepts of permutation and combination for CPT

The CPT or Common Proficiency Test is sometimes also known by the name CA – CPT. It can be defined as an objective test in which the concept of negative marking is present. This is an entry-level exam arranged by ICAI or the Institute of Chartered Accountants of India for getting admission in the course of chartered accountancy. It is a test for 4 main subjects that are mercantile law, accounting, general economics, accounting as well as quantitative aptitudes. The CPT is a 200 marks test divided into 2 sessions of 2 hours each. The concepts of permutation and combination are vital for this exam.

The basic concepts of permutation and combination needed for CPT are the same as those involved in mathematics or more specifically business mathematics. Some examples illustrating the basic combinations of permutation and combinations needed for the CPT exam have been outlined in the following

**Example No. 1:** Evaluate the number of combinations and permutations if r = 3 and n = 12

**Answer:** Given that r = 3 and n = 12.

Using the formula mentioned in previous section Combination is given as

nCr = n! / r! (n-r)! = 12! / 3!(12 -3) ! = 220.

Similarly, the required permutation is

nPr = n! / (n – r)! = 12! / (12 – 3)! = 1320.

**Example No. 2:** Mention the number of ways a committee comprising of 3 women and 5 men can be chosen from 12 women and 9 men

**Answer:** Selecting five men out of the total of nine men in 9C5 ways gives 126 ways

Again, selecting three women out of the total of twelve women in 12C3 ways gives 220 ways.

Selection of the committee can be done in 27720 ways.

### Conclusion

The main subject on which the article has been written is business mathematics. In this subject, the topic that has been discussed throughout the article is permutation and combination. Permutation and combination are some basic concepts in mathematics and are included as some core topics in the syllabus of some important degrees. In this article, the basic concepts of permutation and combination that are needed in BCA and CPT have been properly discussed.