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Why cant insertion stick method be used here

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Source: — Quantitative Reasoning |

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by [email protected] » Sun Mar 09, 2014 10:11 pm
Hi chantahshah,

This question is not worded specifically enough to be considered a GMAT question, so I have to ask what the source is.

The wording doesn't seem to specify whether the "order" of the rings matters or not, not does it include answer choices for reference. Both of these sources of information are useful in interpreting HOW the "math" is supposed to be done.

For example, if rings A and B are on 1 finger, does it matter which ring is put on "first?" Is AB the same as BA (because that WILL affect how you have to do the math)? Questions of this type almost always include language that clarifies this issue, so that any ambiguity can be removed. This prompt doesn't have any of that information, so it's tough to gauge what the intent is.

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by PythaGURUS » Mon Mar 10, 2014 8:32 pm
chintanshah wrote:The question is:
How many ways can 6 rings be worn in 4 fingers of 1 hand.
I feel the answer should be w+x + y + z=6

9!/(3!)(5!)


Is this wrong?
The answer seems to be 4^6
Hi chintanshah,

I totally agree with Rich on the source of this question.

However, I would still want to answer your question. If the official answer is 4^6, then we are making this assumption that you can also wear all four rings in one finger.

Now, every ring can be worn in any of the fingers, so for the first ring there will be four options. Likewise for every ring there will be four options.

Hence, for 6 rings, the answer will be 4x4x4x4x4x4= 4^6

Hope this helps.

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by chintanshah » Mon Mar 10, 2014 9:21 pm
Thanks guys, I too agree that the question is ambiguous, however I saw it in a book and I couldn't wrap my head around it.

Is there any necessary order in which the permutations can be done?
I mean why not do this:

1st finger can have 6 options for the rings
2nd 5 and so on?
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by chintanshah » Mon Mar 10, 2014 9:42 pm
On similar lines, even this confuses me.
Suppose there are 6 coins tossed, how many different outcomes are possible. Now I know from memory that it is 2^64.
However I don't find this illogical.

6 coins are tossed so possible outcomes are
HT HT HT HT HT HT ( For 6 coins- all possible outcomes)

Now I have 6 blanks to fill, since 6 coins will have only 1 true outcome.
Therefore 1st place can be filled in 12 ways, 2nd in 11 ways

Therefore 12x11x10x9x8x7 / (6!6!) (For 6 same heads and 6 same tails)
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by [email protected] » Mon Mar 10, 2014 11:30 pm
Hi chintanshah,

In the coin-toss example, each coin has 2 possible outcomes (heads or tails), so if you have 6 tosses, then there are 2^6 possible permutations (not 2^64).

2^6 = 64 possibilities IF order matters.

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by chintanshah » Mon Mar 10, 2014 11:33 pm
Ya 2^64 was a typing error, Sorry.

Can you explain why my reasoning is fallible?
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by [email protected] » Mon Mar 10, 2014 11:44 pm
Hi chintanshah,

In a permutation question, "order matters", so you have to think about each "event" in the string of events.

With 6 coin tosses, unique outcomes need to be counted. This means that...

HTTTTT is different from TTTTTH.

Since each coin has 2 outcomes, the "math" for the total number of possible outcomes is....

2x2x2x2x2x2 = 64

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by chintanshah » Mon Mar 10, 2014 11:56 pm
Thanks a lot Rich!
That definitely helped clear my doubt.
Thanks to all who replied
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by chintanshah » Thu Mar 13, 2014 5:58 pm
Is there any book that has a comprehensive tutorial of permutations and combinations?
The
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by [email protected] » Thu Mar 13, 2014 11:58 pm
Hi chintanshah,

Other than permutations and combinations, how well are you performing in the Quant section? How have you been scoring on your CATs? While many people have trouble with those categories, they're not likely to be the big categories or the real issues that are costing you points.

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by chintanshah » Fri Mar 14, 2014 12:07 am
Other than permutations and combinations, I guess, decent enough. The thing is permutations and combinations affect my performance in probablity too.
When I solved permutations drill I did pretty well there too, however certain points are just not clear enough, which impairs my ability to really see through permutations and combinations, even questions that I got right the first time, I start having second thoughts about them.
Mainly this n^r concept has me confused.

I just figured if there is one book or one place from where I can get everything properly, then it would be great!
I dont want to leave PnC to hap!
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by Bill@VeritasPrep » Fri Mar 14, 2014 2:45 pm
chintanshah wrote:Is there any book that has a comprehensive tutorial of permutations and combinations?
The
I'm obviously biased, but I think the Veritas book does a great job of simplifying these concepts.

You might also find Khan Academy helpful: https://www.khanacademy.org/math/trigon ... rmutations
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