Permutation And Combination- Definition, Use of Formula & Solved Examples

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About Permutation And Combination

Permutation and combination are the methods for representing a collection of things by picking them from a set and dividing them into subsets. It specifies the numerous methods for organising a set of data. Permutations are used to pick data or objects from a group, whereas combinations are used to represent the order in which they are displayed. Permutation and combination, as well as the differences between them, are thoroughly detailed here.

What do you mean by Permutation?

The permutation is the act of putting all the members of a set into a sequence or order in mathematics. Permuting, in other words, is the process of rearranging the elements of a set that has previously been sorted. Permutations appear in practically every branch of mathematics, in some form or another. When different orderings on finite sets are examined, they frequently appear. Maths Formulas List.

What do you mean by a Combination?

The combination is a method of selecting elements from a set when the order of selection is irrelevant (unlike permutations). The number of possible combinations can be counted in smaller circumstances. The term "combination" refers to the taking of n things k at a time without repeating the process. The words k-selection and k-combination with repetition are frequently used to describe combinations that allow for the repeat.

Permutation and Combination Formulas

Permutation and combination notions involve a lot of formulas. The following are the two important formulas: Permutation Formula

A permutation is the selection of r items from a collection of n items without replacement, with the order of the items being imported.

ⁿP_r = $\frac{(n!)}{(n - r)!}$

Combination Formula

A combination is the selection of r items from a set of n items with no replacements and no regard for order.

${}^{n}C_{r} = \frac{(n!)}{{(n - r)! \times r!}} = \frac{{}^{n}P_{r}}{r!}$

Difference Between Permutation and Combination

Permutation	Combination
Arranging people, digits, numbers, alphabets, letters, and colours	Selection of menu, food, clothes, subjects, team.
Picking a team captain, pitcher and shortstop from a group.	Picking three team members from a group.
Picking two favourite colours, in order, from a colour brochure.	Picking two colours from a colour brochure.
Picking first, second and third place winners.	Picking three winners.

Maths Formulas List.

Permutation And Combination