How to count permutations and combinations
- Enter n, the number of items to choose from, and r, how many you pick.
- Tick Repetition allowed if the same item can be picked more than once, like digits in a PIN.
- Read nCr (order doesn’t matter) and nPr (order matters).
Which one do I need?
| Question | Use |
|---|---|
| How many ways to arrange books on a shelf? | Permutation |
| How many possible PINs or passwords? | Permutation with repetition |
| How many ways to choose a committee? | Combination |
| How many pizza toppings combos, allowing doubles? | Combination with repetition |
n choose k
nCr is also written C(n, r) or as n over r in brackets, read “n choose r”. These numbers make up Pascal’s triangle, and they are the coefficients when you expand (a + b)ⁿ.