Calculate combinations C(n,r) — choosing without order — and permutations P(n,r) — arranging with order. Includes step-by-step factorial working.
Combinations: order does not matter (choosing toppings). Permutations: order matters (race rankings). P(n,r) = C(n,r) × r!
C(10,3) = 10!/(3!×7!) = 120. Ways to choose 3 from 10 when order does not matter.
Combinations: lottery, committees, card hands. Permutations: rankings, PIN codes, seating arrangements.
n! = product of all positive integers up to n. 5! = 120. By definition 0! = 1.
For n distinct letters: n! arrangements. For NOON with repeated letters: 4!/(2!×2!) = 6.