Combination & Permutation Calculator
Calculate the number of combinations (nCr) and permutations (nPr) for choosing r items from a set of n items. Combinations ignore order; permutations consider order.
Combinations and permutations are fundamental concepts in counting and probability.
Permutations (order matters):
nPr = n! / (n-r)!
A permutation counts the number of ways to arrange r items selected from n items. The order of selection matters: ABC is different from BCA.
Combinations (order does not matter):
nCr = n! / (r! × (n-r)!)
A combination counts the number of ways to choose r items from n items without regard to order: {A,B,C} is the same as {B,C,A}.
Key Relationship:
nPr = nCr × r!
Because each combination of r items can be arranged in r! different orders.
Examples:
- Lottery (6 from 49, order irrelevant): C(49,6) = 13,983,816
- Podium finishes (3 from 10 runners): P(10,3) = 720
- Choosing a committee of 4 from 20 people: C(20,4) = 4,845
- Arranging 5 books on a shelf from 8: P(8,5) = 6,720