Combinations vs Permutations
This topic has expert replies
- Ashley@VeritasPrep
- GMAT Instructor
- Posts: 199
- Joined: Tue May 17, 2011 6:06 am
- Location: Cambridge, MA
- Thanked: 192 times
- Followed by:121 members
- GMAT Score:780
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!
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!
Ashley Newman-Owens
GMAT Instructor
Veritas Prep
Post helpful? Mosey your cursor on over to that Thank button and click, please! I will bake you an imaginary cake.
GMAT Instructor
Veritas Prep
Post helpful? Mosey your cursor on over to that Thank button and click, please! I will bake you an imaginary cake.
- vinni.k
- Master | Next Rank: 500 Posts
- Posts: 421
- Joined: Sun Apr 17, 2011 4:27 am
- Location: India
- Thanked: 6 times
- Followed by:2 members
- GMAT Score:620
Hi,zachlebo wrote: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!
Read the following link. It explains difference between permutation and combination.
https://www.manhattangmat.com/strategy-s ... bility.cfm
Hope this helps.
Regards
Vinni
GMAT/MBA Expert
- Ian Stewart
- GMAT Instructor
- Posts: 2621
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
Ashley@VeritasPrep wrote: 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.
Great post - just one very pedantic point about poker hands that is irrelevant on the GMAT (the GMAT will never ask a question about standard card games, because that would give an unfair advantage to test takers familiar with those games) but which I point out in case someone thinks about your example in the context of stud-based poker games (if you don't know anything about poker, there's no reason to read this post). In a game like blackjack, where the dealer is dealt two cards, but one of the cards is face up (so visible to everyone else) and one is face down, you'd normally consider the order of the two cards to be important, since they have different roles: one is visible and one is invisible to the other players. The same is true in some forms of poker like 7-card stud or razz. Your starting hand in those games consists of three cards, one of which is visible to everyone else, and the other two of which are visible only to you. Then you would consider order to be partly important; having an Ace showing makes your hand look better than having an 8 showing.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com