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question about combinations and permusation

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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question about combinations and permusation

by svbla » Fri Apr 01, 2016 12:28 pm
I have two questions don't get it. can someone explain here? thanks!


5. How many different four-letter passwords can be created for a software access if no letter can be used more than once?

6.How many different ways you can elect a Chairman and Co-Chairman of a committee if you have 10 people to choose from.

my answer were:
5: 26C4
6: 10C2

because I don't think the order matters here, it didn't say anything about orders!
well the correct answers are 26P4 and 10P2.

Can someone explain it to me why the order matters in these two questions??
Thanks!!
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by [email protected] » Fri Apr 01, 2016 2:26 pm
Hi svbla,

If these are GMAT questions, then you should make sure to list the 5 answer choices. In addition, you should list questions individually, so that the discussion can stay focused on one prompt.

Regarding these two prompts, they are both Permutations (since the order of the items matters.

In question #5, passwords are unique (meaning that "abcd" is NOT the same as "dcba"), so the number of passwords (if letters CANNOT be used more than once) is (26)(25)(24)(23)

In question #6, the two "titles" are "Chairman" and "Co-Chairman", so choosing "A" for chairman and "B" for co-chairman is NOT the same as choosing "B" for chairman and "A" for co-chairman. As such, the possible arrangements are (10)(9) = 90.

IF... in question #6, you were selecting two "co-chairman" (meaning that both people would receive the same title), THEN you would have a Combination and the answer would be 10c2.

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by ceilidh.erickson » Sat Apr 02, 2016 12:43 pm
As Rich pointed out, order DOES matter in both of these cases. Here's a way to help you remember...

Order DOESN'T matter if you could shuffle all of the positions around and still have the same grouping. The terms that will be most often used here:
- GROUP
- COMMITTEE
- TEAM
- MIXTURE (e.g. adding items to a fruit salad)

Order DOES matter whenever specific positions are specified / implied. Here are the most common types:
- PASSWORD COMBINATIONS
- ARRANGEMENTS (pictures on a wall, people in a seating chart, letters in a word, etc)
- RANKINGS (gold/silver/bronze, 1st/2nd/3rd place finish, president/vice president, etc)
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by Matt@VeritasPrep » Thu May 11, 2017 8:24 pm
The order definitely matters! If Mark is the chairman and Dave is the co-chairman, we've got a different leadership team than we'd have if Dave is the chairman and Mark is the co-chairman: in the first case, Mark has final say, but in the second, Dave does.

So many of the problems in the world come down to this, don't they? :)
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by ceilidh.erickson » Mon Jun 05, 2017 6:35 pm
Matt@VeritasPrep wrote:The order definitely matters! If Mark is the chairman and Dave is the co-chairman, we've got a different leadership team than we'd have if Dave is the chairman and Mark is the co-chairman: in the first case, Mark has final say, but in the second, Dave does.

So many of the problems in the world come down to this, don't they? :)
Hm, yes - I'd say that a lot of the problems in the world come down to all-male leadership teams ;)
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by Matt@VeritasPrep » Mon Jun 05, 2017 11:56 pm
ceilidh.erickson wrote: Hm, yes - I'd say that a lot of the problems in the world come down to all-male leadership teams ;)
Hey, if they're chairman and co-chairman of, say, the Flat Earth Society, I'd think we want the most problematic leadership possible. ó"¿Ã³
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by elias.latour.apex » Mon Jun 19, 2017 3:22 am
ceilidh.erickson wrote:
Matt@VeritasPrep wrote:The order definitely matters! If Mark is the chairman and Dave is the co-chairman, we've got a different leadership team than we'd have if Dave is the chairman and Mark is the co-chairman: in the first case, Mark has final say, but in the second, Dave does.

So many of the problems in the world come down to this, don't they? :)
Hm, yes - I'd say that a lot of the problems in the world come down to all-male leadership teams ;)
Are you assuming their gender?
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by Matt@VeritasPrep » Wed Jun 21, 2017 4:25 pm
elias.latour.apex wrote:
ceilidh.erickson wrote:
Matt@VeritasPrep wrote:The order definitely matters! If Mark is the chairman and Dave is the co-chairman, we've got a different leadership team than we'd have if Dave is the chairman and Mark is the co-chairman: in the first case, Mark has final say, but in the second, Dave does.

So many of the problems in the world come down to this, don't they? :)
Hm, yes - I'd say that a lot of the problems in the world come down to all-male leadership teams ;)
Are you assuming their gender?
You know, I pondered that riff myself, but I couldn't find any languages/cultures in which Mark and Dave were female names. (You'd think Davé would be a female name somewhere, but I couldn't find it.)
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by elias.latour.apex » Thu Jun 22, 2017 3:54 am
Matt@VeritasPrep wrote:
elias.latour.apex wrote:
ceilidh.erickson wrote:
Matt@VeritasPrep wrote:The order definitely matters! If Mark is the chairman and Dave is the co-chairman, we've got a different leadership team than we'd have if Dave is the chairman and Mark is the co-chairman: in the first case, Mark has final say, but in the second, Dave does.

So many of the problems in the world come down to this, don't they? :)
Hm, yes - I'd say that a lot of the problems in the world come down to all-male leadership teams ;)
Are you assuming their gender?
You know, I pondered that riff myself, but I couldn't find any languages/cultures in which Mark and Dave were female names. (You'd think Davé would be a female name somewhere, but I couldn't find it.)
You're mistaken because you are confusing gender with GMAT. They are not the same. Dave could easily be a pre-op transgender woman trapped in a man's body.
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