Hi, I have been using the Manhattan Guides and these topics have just come up. I am wondering when to use either the Comb or Permut formulat. If there are any links for the basics, that would be great!
Hey Zach,
Do you mean how do you know which to use? If so, basically, you use the permutation formula if order is a relevant concern (i.e. if changing the order would result in a legitimately different scenario), and you use the combination formula if all you care about is what/who you wind up with, and not how those things are arranged. Some examples:
How many different poker hands are possible? --> Combination, because all you care about is what cards are in your hand... arranging them in a different order does not create a different situation.
How many different ways can the competitors place in the race --> Permutation, because if A gets 1st place and B gets 2nd and C gets 3rd, that's a different scenario from if A gets 1st and C gets 2nd and B gets 3rd.
How many different ways can I arrange the vases in a row on the mantle? --> A permutation
I'm packing four shirts for a trip. I own 15 shirts. How many different combinations of four shirts to bring are possible? --> Combination, because they'll all get jumbled together in my suitcase. Order is irrelevant.
I've packed four shirts for a trip. In how many different orders can I wear them? --> Permutation, since, by my specifications, I want to count Day 1 Stripes, Day 2 Plaid, Day 3 Red, Day 4 Polka-dots as a different scenario from Day 1 Stripes, Day 2 Plaid, Day 3 Polka-dots, Day 4 Red.
But I may have misunderstood your question and you not have actually been asking how to distinguish between the two. If that's the case, my apologies!
