Calculator Inputs
Results
120
Combinations (nCr)
720
Permutations (nPr)
About This Calculator
Combinations (nCr) count ways to choose r items from n where order does not matter. Permutations (nPr) count arrangements where order does matter.
Formulas
- nCr = n! ÷ (r! · (n−r)!)
- nPr = n! ÷ (n−r)!
Because nCr ≤ nPr for any r, order always creates more possibilities.
Frequently Asked Questions
When do I use combinations vs permutations?
Use combinations when the order of selection does not matter (e.g. a lottery draw). Use permutations when order matters (e.g. podium finishes: gold, silver, bronze).
Why is choosing 0 or all items equal to 1?
There is exactly one way to choose nothing (choose none) and exactly one way to choose everything. Both nC0 and nCn equal 1.