Difference between Permutation and Combination
Permutation involves arranging a set of objects in a particular order, while combination involves selecting a subset of objects from a larger set without regard to order.
Permutation Vs Combination
|Order matters and the arrangement of members is important||Order matters, and the arrangement of members is important|
|n! / (n-r)!||n! / r!(n-r)!|
|nPr or P(n,r)||nCr or C(n,r)|
|Arranging 4 books on a shelf in different orders||Selecting 4 books from a shelf without considering their order|
|nPr = n! / (n-r)! where n is the total number of objects and r is the number of objects selected||nCr = n! / r!(n-r)! where n is the total number of objects and r is the number of objects selected|
4 Difference between Permutation and Combination
- Permutation considers the order of elements, while combination does not.
- A permutation is used when the arrangement or order of elements is important, while a combination is used when only the selection of elements matters.
- The permutation is denoted as nPr or P(n,r), while the combination is denoted as nCr or C(n,r).
- The formula for permutation is n! / (n-r)!, while the formula for combination is n! / r!(n-r)!.