Permutation Calculator
Discover simple permutations (P) and arrangements (A).
Permutation vs Arrangement: What is the difference?
In combinatorial analysis, the keyword of these two formulas is the same:The order matters.
Simple Permutation (Pn)
In permutation, we use ALL the available elements and just swap their places (we \"permute\"). If we have 5 people (n=5) and 5 empty chairs in the cinema, in how many ways can they sit? The calculation is simply the factorial of the total (5!), which gives 120. On our calculator, just fill in the Total (n) and leave the \"Groups (p)\" box empty to calculate Simple Permutations.
Simple Arrangement A(n,p)
An Arrangement occurs when you do not use all the available elements, but the order still matters. Example: A race with 10 Formula 1 cars. The podium has only 3 places (1st, 2nd, 3rd). The order of the podium matters (winning gold is not the same as winning bronze!). Therefore, you have n=10 total cars and p=3 spots. Using a calculator, we find that there are 720 different ways that podium can happen.