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21 Sep 2007, 19:21
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These are relatively simple problems.
Despite my ability to solve most combinations problems I still can't quite grasp this fundamental aspect of combinatorics questions.
Essentially when Does order matter and when does it NOT matter?
Ex/ If there are 7 people in a room, but only 4 chairs available, how many different seating arrangements are possible?
Ex2/ If a team of 4 people is to be chosen from 7 people in a room, how many different teams are possible?
I know what to do for these two problems, so please don't just give the solutions for these. Explain Why one has to be one way and the other a different way.
If I ever get Ex2 I know exactly what to do. Anything with "team" I know exactly what to do.
Ex 1/ however, I wouldn't always know to solve by doing 7!/3!.
Thanks
Despite my ability to solve most combinations problems I still can't quite grasp this fundamental aspect of combinatorics questions.
Essentially when Does order matter and when does it NOT matter?
Ex/ If there are 7 people in a room, but only 4 chairs available, how many different seating arrangements are possible?
Ex2/ If a team of 4 people is to be chosen from 7 people in a room, how many different teams are possible?
I know what to do for these two problems, so please don't just give the solutions for these. Explain Why one has to be one way and the other a different way.
If I ever get Ex2 I know exactly what to do. Anything with "team" I know exactly what to do.
Ex 1/ however, I wouldn't always know to solve by doing 7!/3!.
Thanks
22 Mar 2015, 12:59
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Hi All,
While this is an old post, it represents an issue that impacts many Test Takers. Permutations and Combinations are relatively rare categories on Test Day. You'll probably see at least 1 of each, but even if you're performing really well in the Quant section you likely won't see more than 2-3 of each. While they generally appear as higher-level concepts, some of these questions are rather easy to solve IF you understand how the math "works."
The 'big' difference between these two question types is about 'order' - when reading through the question, you have to ask yourself IF order 'matters'. If it does, then it's a Permutation question; if it does NOT, then it's a Combination question. Thankfully, the questions themselves often offer clues (e.g. the word "arrangement" means Permutation, the word "combinations" means Combination).
The first example isn't written very clearly, since it does not describe how the chairs are arranged. If they're in a row, then THAT fact (combined with the word "arrangements") makes this a pretty straight-forward Permutation question. However, if the chairs were arranged around a table (for example), then the math that you would have to do would differ ('circular arrangements' are more complex).
In the second example, we're forming "teams" without granting any individual person a special "title/rank." In this situation, we're grouping people, so the group ABCD is the same as the group BCAD. In this way, order does NOT matter and we have a Combination question.
GMAT assassins aren't born, they're made,
Rich
While this is an old post, it represents an issue that impacts many Test Takers. Permutations and Combinations are relatively rare categories on Test Day. You'll probably see at least 1 of each, but even if you're performing really well in the Quant section you likely won't see more than 2-3 of each. While they generally appear as higher-level concepts, some of these questions are rather easy to solve IF you understand how the math "works."
The 'big' difference between these two question types is about 'order' - when reading through the question, you have to ask yourself IF order 'matters'. If it does, then it's a Permutation question; if it does NOT, then it's a Combination question. Thankfully, the questions themselves often offer clues (e.g. the word "arrangement" means Permutation, the word "combinations" means Combination).
The first example isn't written very clearly, since it does not describe how the chairs are arranged. If they're in a row, then THAT fact (combined with the word "arrangements") makes this a pretty straight-forward Permutation question. However, if the chairs were arranged around a table (for example), then the math that you would have to do would differ ('circular arrangements' are more complex).
In the second example, we're forming "teams" without granting any individual person a special "title/rank." In this situation, we're grouping people, so the group ABCD is the same as the group BCAD. In this way, order does NOT matter and we have a Combination question.
GMAT assassins aren't born, they're made,
Rich
22 Sep 2007, 03:21
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Bookmarks
just keep in mind dis thing
wen der is arrangement of chairs, alphabets etc its a problem of permutation
n
wen v hav to select from group of ppl, no. of balls etc its a problem on combination
Ex1 says dat v need to arrange 7 ppl in 4 chairs so dat'll b 7P4
Ex2 says v need to select 4 ppl from 7 so dat'll b 7C4
remember-- for permutation problems always use 'P' n for combination problems always use 'C' i guess dat'll b simple to remember
so u can try it out on any problem
for ex. 2 cards r to be selected out of the deck so that both of dem r of hearts
here imp word is 'select' d moment u c dis word u shud know dat dis problem is of selection hence use 'C' so it'll b 13c2/52c2
hope dis little piece of advice helps
wen der is arrangement of chairs, alphabets etc its a problem of permutation
n
wen v hav to select from group of ppl, no. of balls etc its a problem on combination
Ex1 says dat v need to arrange 7 ppl in 4 chairs so dat'll b 7P4
Ex2 says v need to select 4 ppl from 7 so dat'll b 7C4
remember-- for permutation problems always use 'P' n for combination problems always use 'C' i guess dat'll b simple to remember
so u can try it out on any problem
for ex. 2 cards r to be selected out of the deck so that both of dem r of hearts
here imp word is 'select' d moment u c dis word u shud know dat dis problem is of selection hence use 'C' so it'll b 13c2/52c2
hope dis little piece of advice helps
