How it is calculated
Combinations do not care about the order of the items chosen. Arrangements do. A permutation takes all n items and only changes their order.
C(n, k) = n! / (k! (n − k)!)
Where the numbers come from
- Total items
- How many to pick
Example
From 5 items taken 2 at a time: 10 combinations, 20 arrangements, and 120 permutations of all five.
Questions
Why are there fewer combinations than permutations?
The pair “first and second” is one combination. As an arrangement, it is two different orders.
Is k greater than n?
That pick is not allowed, and the calculator will stop.
Do permutations disappear at large n?
The exact n! is shown up to 18. Combinations keep going for as long as the precision holds.