The Video tutorial by The Organic Chemisty Tutor explains permutations and combinations. It contains a few word problems including one associated with the fundamental counting principle. Permutations are useful to determine the different number of ways to arrange something where as combinations is useful for determining how many ways to combine something when the order does not matter such as selecting members to form a committee. In a permutation, the order matters. This video also discusses the basics of permutations and combinations using letters such as ABCD.
What is Permutation?
In mathematics, permutation relates to the act of arranging all the members of a set into some sequence or order. In other words, if the set is already ordered, then the rearranging of its elements is called the process of permuting. Permutations occur, in more or less prominent ways, in almost every area of mathematics. They often arise when different orderings on certain finite sets are considered. (Byju’s Tutorial)
What is a Combination?
The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. In smaller cases, it is possible to count the number of combinations. Combination refers to the combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-selection or k-combination with repetition are often used. (Byju’s Tutorial)
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. |
