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Permutation and combination are two of the most crucial terms studied in higher classes. In simple terms, Permutations are arrangements, while combinations are referred to as choices. These are mainly used for counting the number of alternative outcomes in several mathematical scenarios. In order to closely understand permutation and combination, the concept of factorials must be remembered. The term “n” is equal to the product of the first n natural numbers in permutation and combination.
This article talks about permutation and combination. You will find brief information on the concept of the permutation and combination in maths, formulas of permutation and combination, their differences, and so on. So, let’s start by describing permutation and combination in the Maths study material.
Permutation: Definition
In mathematics, permutation can be described as arranging numbers of an object in a specific order taken one at a time or all at once. Let’s understand permutation through a simple example. Imagine the following ten numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. P(10,4) = 5040 is the number of different 4-digit-PINs that may be constructed using these 10 digits.
Combination: Definition
In mathematics, the combination can be described as a method used for calculating the number of possible groups, which can be constructed from any of the available items. Further, below, we have divided the example of combination into two major categories –
Case 1 where it is permitted, such as in the case of coins in your pocket (2,5,5,10,10)
Case 2 where it is not permitted: Lottery numbers, for example, are not allowed to be repeated (2,14,18,25,30,38)
Permutation and Combination formulae
There are a number of formulas involved in permutation and combination. The following are two important formulas:
Formula for permutation
A permutation is the selection of r items from a collection of n items without replacement, with the order of the items being imported.
nPr = (n!) / (n-r)!
The formula for combination
A combination is a selection of r items from a set of n items with no replacements and no regard for order.
Examples of Permutation and Combination
Here are quick examples of permutation and combination for ease of understanding.
Question 1: If n = 15 and r = 3, calculate the number of permutations and combinations.
Solution: n is equal to 15, r is equal to 3 (Given)
Using the formulas for permutation and combination, we get:
Permutation, nPr = n!/(n – r)!
= 15!/(15 – 3)!
= 15!/12!
= (15 x 14 x 13 x 12!)/12!
= 15 x 14 x 13
= 2730
Additionally, Combination, nCr = n!/(n – r)!r!
= 15!/(15 – 3)!3!
= 15!/12!3!
= (15 x 14 x 13 x 12! )/12!3!
= 15 x 14 x 13/6
= 2730/6
= 455
Question 2: An event organiser has ten chair designs and eight table patterns. How many different ways can he create a set of tables and chairs?
Solution: The event planner features ten chair patterns and eight table patterns.
There are ten different ways to choose a chair.
A table can be chosen in eight different ways.
As a result, one chair and one table can be chosen in ten different ways.
= 80 different ways
Difference between Permutation and Combination
Here are the quick differences between permutation and combination –
Permutation | Combination |
When an order/sequence of arrangement is required, permutations are utilized. | When simply the number of feasible groups needs to be identified, and the order/sequence of arrangements isn’t important, combinations are employed. |
Permutations are utilized for a variety of things. | Combinations are used to describe similar items. |
Ab, ba, bc, cb, ac, ca is the permutation of two items from three given things a, b, c. | Ab, bc, ca is a combination of two things from three given things a, b, and c. |
It could be said that for a multitude of arrangements of things nPr=n!/(n-r)!. | On the other hand, for different possible selections of things, nCr =n!/r!(n-r)!. |
The permutation response is larger than the combination answer for a given set of n and r values. | The combination response is smaller than the permutation answer for a given set of n and r values. |
Conclusion
With this, we come to an end to permutation and combination. When you study Maths, permutation and combination are mostly taught in higher classes due to the complexity involved since they both are used in a variety of contexts. Combinations are a type of counting used to select r different objects from a set of n different objects. Whereas, Permutations are counting used to arrange r different objects out of n different objects. Today, in this study material, we thoroughly studied the concepts of permutation and combination.
In this article describing permutation and combination, we studied the concept of the permutation and combination in length. We covered several other topics, such as the formulas of permutation and combination, differences between permutation and combination, and other related topics. We hope this study material must have helped you better understand the permutation and combination.
