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

Permutation	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)!.