Permutation and Combination Calculator

1. Enter n, the total number of items in the set. For example, if you have 10 candidates for 3 positions, n = 10.
2. Enter r, the number of items being chosen or arranged. For 3 positions chosen from 10, r = 3.
3. Permutation counts ordered arrangements. Choosing president, vice president, and treasurer from 10 people is a permutation because the order (who gets which role) matters.
4. Combination counts unordered selections. Choosing 3 people for a committee from 10 is a combination because the order does not matter.

n is limited to 20 because factorials grow extremely fast (20! = 2,432,902,008,176,640,000).

Permutation (order matters):
  P(n, r) = n! / (n - r)!

Combination (order does not matter):
  C(n, r) = n! / [r! × (n - r)!]

Relationship: P(n, r) = C(n, r) × r!
  Each combination can be arranged in r! ways to form permutations.

Example with n=10, r=3:
  P(10, 3) = 10! / 7! = (10×9×8×7!) / 7! = 10×9×8 = 720
  C(10, 3) = 10! / (3! × 7!) = 720 / 6 = 120

Memory tip:
  P for Positions (order matters)
  C for Committee (order doesn't matter)
  C = P / r! because dividing by r! removes order