Elements of Combinatorics - Permutations, Arrangements, Combinations

Combinatorics is a branch of mathematics that studies questions about how many different combinations, subject to certain conditions, can be formed from given objects.

Choosing objects and arranging them in a certain order is a task encountered in almost all areas of human activity, for example, a designer developing the distribution of agricultural crops over several fields.

This online calculator calculates the following combinatorial values:

• Number permutations of n elements: P_n = n!
• Number arrangements of n to k:  A_n^k  = n·(n-1)·(n-2)·...·(n-k+1) = n!/(n-k)!
• Number of combinations of n to k: C_n^k = n! / [k!·(n-k)!]