Permutation and Combination Calculator (nPr & nCr)
Compute nPr (ordered arrangements) and nCr (unordered selections) with full factorial working.
Result
10P3 (Permutations)
720
10C3 (Combinations)
120
nPr / nCr ratio
6 (= r!)
Concept
A permutation is an ordered arrangement — ABC and BAC are different. A combination is an unordered selection — ABC and BAC are the same.
The factorial (n!) counts all ways to arrange n objects; dividing by (n−r)! removes the arrangements of the unchosen objects; dividing further by r! removes duplicates within the chosen group (giving combinations).
Practical rule: if order matters use nPr, if order doesn't matter use nCr.
Formula
nPr=n !(n − r) !
nCr=n !r ! × (n − r) !
Variables
n- Total number of items in the set.
r- Number of items chosen or arranged.
n!- n factorial = n × (n−1) × ... × 1, with 0! = 1.
nPr- Ordered arrangements of r items from n.
nCr- Unordered selections of r items from n.