Enter the Values(n & r)
Number of sample points in set ( n ).
Number of sample points in each combination ( r ).
Calculating the Number of combinations (n things taken r at a time)
What is Factorial: n! ways of arranging n distinct objects into an ordered sequence, permutations where n = r.
What is Permutations: arrangement of all or part of a set of objects, with regard to the order of the arrangement.
What is Combinations: the number of ways to select a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.
Easy calculator for Permutation. Simple Calculator for Permutation and Combination
Permutations count ordered selections: nPr = n! / (n − r)!. Combinations count selections where order does not matter: nCr = n! / (r! × (n − r)!).
For n = 5 and r = 2, there are 20 ordered selections and 10 unordered selections. These formulas assume distinct items and no replacement.
Use whole numbers with 0 ≤ r ≤ n. This calculator limits n to 500 to keep calculations manageable. Selecting zero items gives one selection.
