🔢 Permutation & Combination
nPr (order matters) · nCr (order does not)
When to Use Which
Permutation (order matters)
Lock combinations, race placements, seating arrangements, phone numbers, license plates
Lock combinations, race placements, seating arrangements, phone numbers, license plates
Combination (order does NOT matter)
Lottery picks, team selection, pizza toppings, committee formation, card hands
Lottery picks, team selection, pizza toppings, committee formation, card hands
Permutation vs Combination
Both count ways to choose r items from n items. The difference: permutations care about order (ABC is different from CBA), combinations do not (ABC = CBA). Permutation formula: nPr = n! / (n-r)!. Combination formula: nCr = n! / (r!(n-r)!). Combinations are always smaller because multiple orderings collapse into one group.
Example: choosing 3 people from 10 for president, VP, and secretary (order matters) = 10P3 = 720 ways. Choosing 3 people from 10 for a committee (order does not matter) = 10C3 = 120 ways. There are 6x fewer combinations because each group of 3 can be arranged in 3! = 6 ways.