answersLogoWhite

0

Combination Formula Proof

GENERIC:

  • Let C(n,r) be the number of ways to generate unordered combinations
  • The number of ordered combinations (i.e. r-permutations) is P(n,r)
  • The number of ways to order a single one of those r-permutations P(r,r)
  • The total number of unordered combinations is the total number of ordered combinations (i.e. r-permutations) divided by the number of ways to order each combination
  • Thus, C(n,r) = P(n,r)/P(r,r) = [n!/(n-r)!]/r!/(r-r)!] = n!/r!(n(n-r)!

SPECIFIC:

  • Let C(52,5) be the number of ways to generate unordered Poker hands
  • The number of ordered poker hands is P(52,5) = 311,875,200
  • The number of ways to order a single poker hand is P(5,5) = 5! = 120
  • The total number of unordered poker hands is the total number of ordered hands divided by the number of ways to order each hand
  • Thus, C(52,5) = P(52,5)/P(5,5)
User Avatar

Wiki User

14y ago

Still curious? Ask our experts.

Chat with our AI personalities

CoachCoach
Success isn't just about winning—it's about vision, patience, and playing the long game.
Chat with Coach
DevinDevin
I've poured enough drinks to know that people don't always want advice—they just want to talk.
Chat with Devin
SteveSteve
Knowledge is a journey, you know? We'll get there.
Chat with Steve

Add your answer:

Earn +20 pts
Q: How can you prove the combination formula?
Write your answer...
Submit
Still have questions?
magnify glass
imp