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!!
question about combinations and permusation
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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.
GMAT assassins aren't born, they're made,
Rich
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.
GMAT assassins aren't born, they're made,
Rich
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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)
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)
Ceilidh Erickson
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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?
So many of the problems in the world come down to this, don't they?
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Hm, yes - I'd say that a lot of the problems in the world come down to all-male leadership teamsMatt@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?
Ceilidh Erickson
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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"¿Ã³ceilidh.erickson wrote: 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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Are you assuming their gender?ceilidh.erickson wrote:Hm, yes - I'd say that a lot of the problems in the world come down to all-male leadership teamsMatt@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?
Elias Latour
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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.)elias.latour.apex wrote:Are you assuming their gender?ceilidh.erickson wrote:Hm, yes - I'd say that a lot of the problems in the world come down to all-male leadership teamsMatt@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?
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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.Matt@VeritasPrep wrote: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.)elias.latour.apex wrote:Are you assuming their gender?ceilidh.erickson wrote:Hm, yes - I'd say that a lot of the problems in the world come down to all-male leadership teamsMatt@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?
Elias Latour
Verbal Specialist @ ApexGMAT
blog.apexgmat.com
+1 (646) 736-7622
Verbal Specialist @ ApexGMAT
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