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A password to a certain database consists of digits that can

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A password to a certain database consists of digits that cannot be repeated. If the password is known to consist of at least 8 digits and it takes 12 seconds to try one combination, what is the amount of time, in minutes, necessary to guarantee access to database?

A. 8!/5
B. 8!/2
C. 8!
D. 10!/2
E. 5/2.10!
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Sep 2012, 06:34, edited 3 times in total.
Renamed the topic and edited the question.

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Re: Permutation and Combination [#permalink]

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sumana wrote:
A password to a certain database consists of digits that cannot be repeated.If the password is known to consist of 8 digits and it takes 12 seconds to try one combination , what is the amount of time , in minutes , necessary to guarantee access to database?


Hi, and welcome to the Gmat Club. Below is the solution for your problem.

Total # of passwords possible is \(P^8_{10}=10*9*8*7*6*5*4*3\) (picking 8 different digits out of ten when order of the digits matters, or another approach 10 choices for the 1st digit, 9 choices for the second and so on), 1/5 minute (12 seconds) for one combination, means that time needed to guarantee access to database is \(\frac{P^8_{10}}{5}\) minute.

Hope it's clear.
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Re: Permutation and Combination [#permalink]

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New post 08 Jun 2010, 11:53
Bunuel wrote:
sumana wrote:
A password to a certain database consists of digits that cannot be repeated.If the password is known to consist of 8 digits and it takes 12 seconds to try one combination , what is the amount of time , in minutes , necessary to guarantee access to database?


Hi, and welcome to the Gmat Club. Below is the solution for your problem.

Total # of passwords possible is \(P^8_{10}=10*9*8*7*6*5*4*3\) (picking 8 different digits out of ten when order of the digits matters, or another approach 10 choices for the 1st digit, 9 choices for the second and so on), 1/5 minute (12 seconds) for one combination, means that time needed to guarantee access to database is \(\frac{P^8_{10}}{5}\) minute.

Hope it's clear.


Thank you - But the answer choices are as follows -

a) 8!/5 b) 8!/2 c) 8! d) 10!/2 and e) 5/2.10!

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Re: Permutation and Combination [#permalink]

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sumana wrote:
Bunuel wrote:
sumana wrote:
A password to a certain database consists of digits that cannot be repeated.If the password is known to consist of 8 digits and it takes 12 seconds to try one combination , what is the amount of time , in minutes , necessary to guarantee access to database?


Hi, and welcome to the Gmat Club. Below is the solution for your problem.

Total # of passwords possible is \(P^8_{10}=10*9*8*7*6*5*4*3\) (picking 8 different digits out of ten when order of the digits matters, or another approach 10 choices for the 1st digit, 9 choices for the second and so on), 1/5 minute (12 seconds) for one combination, means that time needed to guarantee access to database is \(\frac{P^8_{10}}{5}\) minute.

Hope it's clear.


Thank you - But the answer choices are as follows -

a) 8!/5 b) 8!/2 c) 8! d) 10!/2 and e) 5/2.10!


Answer to the question you've posted is \(\frac{P^8_{10}}{5}\), which can also be written as \(\frac{10!}{10}=9!\). But still no match with any of the answer choices. Pleas check the question (maybe some info from the stem is missing) or site the source.
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Re: Permutation and Combination [#permalink]

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New post 08 Jun 2010, 12:34
Quote:
Hi, and welcome to the Gmat Club. Below is the solution for your problem.

Total # of passwords possible is \(P^8_{10}=10*9*8*7*6*5*4*3\) (picking 8 different digits out of ten when order of the digits matters, or another approach 10 choices for the 1st digit, 9 choices for the second and so on), 1/5 minute (12 seconds) for one combination, means that time needed to guarantee access to database is \(\frac{P^8_{10}}{5}\) minute.

Hope it's clear

Thank you - But the answer choices are as follows -

a) 8!/5 b) 8!/2 c) 8! d) 10!/2 and e) 5/2.10!


Quote:

Answer to the question you've posted is \(\frac{P^8_{10}}{5}\), which can also be written as \(\frac{10!}{10}=9!\). But still no match with any of the answer choices. Pleas check the question (maybe some info from the stem is missing) or site the source.



Source is Veritas material

I did check the question and following info is missing - If the password is known to consist of at least 8 digits - "at least" is missing

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Re: Permutation and Combination [#permalink]

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sumana wrote:
Quote:
Hi, and welcome to the Gmat Club. Below is the solution for your problem.

Total # of passwords possible is \(P^8_{10}=10*9*8*7*6*5*4*3\) (picking 8 different digits out of ten when order of the digits matters, or another approach 10 choices for the 1st digit, 9 choices for the second and so on), 1/5 minute (12 seconds) for one combination, means that time needed to guarantee access to database is \(\frac{P^8_{10}}{5}\) minute.

Hope it's clear

Thank you - But the answer choices are as follows -

a) 8!/5 b) 8!/2 c) 8! d) 10!/2 and e) 5/2.10!


Quote:

Answer to the question you've posted is \(\frac{P^8_{10}}{5}\), which can also be written as \(\frac{10!}{10}=9!\). But still no match with any of the answer choices. Pleas check the question (maybe some info from the stem is missing) or site the source.



Source is Veritas material

I did check the question and following info is missing - If the password is known to consist of at least 8 digits - "at least" is missing


I see. This "at least" changes everything, it means that password can have 8, 9 or 10 digits (more than 10 is not possible as per stem digits must be distinct).

Total # of passwords possible for 8 digits is \(P^8_{10}=\frac{10!}{2}\);
Total # of passwords possible for 9 digits is \(P^9_{10}=10!\);
Total # of passwords possible for 10 digits is \(P^{10}_{10}=10!\).

Time needed to guarantee access to database is \((\frac{10!}{2}+10!+10!)*\frac{1}{5}=\frac{10!}{2}\) minutes.

Answer: D.
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Re: Permutation and Combination [#permalink]

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New post 08 Jun 2010, 22:01
Bunuel,
I used combination for this problem since the qs uses the word comb. I thought when the qs doesn't indicate anything about the order then we have to assume that it doesn't matter. Please correct me.

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Re: Permutation and Combination [#permalink]

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bibha wrote:
Bunuel,
I used combination for this problem since the qs uses the word comb. I thought when the qs doesn't indicate anything about the order then we have to assume that it doesn't matter. Please correct me.


Most combinatorics questions can be solved with different approaches. Did you get correct answer with your approach? If yes, then it doesn't matter which formula you used.

Next, it's a password, of course order matters: 12345678 is different from 87654321. \(P^8_{10}\) directly gives the total # of 8 digit passwords (when digits are distinct), because it counts every case of 8 digits possible from 10 (eg the case of "12345678") as many times as the digits can be arranged there (87654321, 56781234, ...). Different way to get the same answer: \(C^8_{10}\) # of ways to choose 8 digits out of 10 multiplied by 8! to get different arrangements of these digits, so \(C^8_{10}*8!\), which is the same as \(P^8_{10}\) (\(C^8_{10}*8!=P^8_{10}\)).

Combinatorics questions are often confusing for many and there are numerous resources with really strange (not to say more) advices, like "if there is some specific word in stem (eg "combination") then use C" or "if there is a direct indication that order matters then use P" and so on.

I think one should understand the formula and not just memorize it. When solving the question we should first understand what it is about and only after that choose the proper tool (formula) and not first choose formula (based on one word) and then trying to squeeze numbers in it.

Hope it helps.
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Re: Permutation and Combination [#permalink]

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New post 09 Jun 2010, 07:44
sumana wrote:
Thank you.


Could you please correct your first port ? As you said, the stem is missing the "at least" and you forgot to put the answer choices.

Thanks.

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P and C ... how to do? [#permalink]

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New post 19 Aug 2010, 00:26
A password contains at least 8 distinct digits. It takes 12 seconds to try one combination, what is the
minimum amount of time required to guarantee access to the database?

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Re: P and C ... how to do? [#permalink]

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New post 19 Aug 2010, 01:03
The questions seems awkward...
Anyways, I will consider that password consists of 8 distinct digits (and of 8 numbers only).
So there will be 8! different passwords and hence the minimum time to access the database is 8! * 12.

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Re: P and C ... how to do? [#permalink]

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New post 19 Aug 2010, 01:51
praveengmat wrote:
A password contains at least 8 distinct digits. It takes 12 seconds to try one combination, what is the
minimum amount of time required to guarantee access to the database?



Key word here is AT LEAST 8 digits,

case (1): When we have exactly 8 digits in the password

Then the number of passwords = \(10_P_8\)

case (2) : When we have 9 digits in the password

Then the number of passwords = \(10_P_9\)

case (3) : When we have all the digits i.e 10 digits in the password

Then the number of passwords = \(10_P_{10}\)

Total number of passwords to\(10_P_8 + 10_P_9 + 10_P_{10}\)

Time taken to crack 1 password \(= 12 seconds\)

Thus, total time \(= (10_P_8 + 10_P_9 + 10_P_{10})*12\)

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Re: Permutation and Combination [#permalink]

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New post 17 Sep 2012, 05:14
Hi bunuel,


In this question we consider 10 digits 0-9

but for a 8 digit number, the first digit cannot be 0 so there would be only 9 ways to select the first digit.

Have we missed that here??
Please explain...

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Re: Permutation and Combination [#permalink]

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New post 17 Sep 2012, 11:20
shankar245 wrote:
Hi bunuel,


In this question we consider 10 digits 0-9

but for a 8 digit number, the first digit cannot be 0 so there would be only 9 ways to select the first digit.

Have we missed that here??
Please explain...


It is a password which consists of at least 8 digits, not an eight-digit number, so it can also start with a 0.
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Re: A password to a certain database consists of digits that can [#permalink]

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sumana wrote:
A password to a certain database consists of digits that cannot be repeated. If the password is known to consist of at least 8 digits and it takes 12 seconds to try one combination, what is the amount of time, in minutes, necessary to guarantee access to database?

A. 8!/5
B. 8!/2
C. 8!
D. 10!/2
E. 5/2.10!


I think the question is flawed.
Let me chalk out the conditions according to the question's language.

Condition 1 - Password contains at least 8 digits
Condition 2 - All the digits of the password are different.

For both the conditions to be satisfied, there can be three cases.

Case 1 - 8 distinct digits. Bunuel has solved this part.

Case 2 - 9 distinct digits. This will be given by

\(10*9*8*.....*2\) = \(10!\)

To try each permutation 1/5 of a minute is needed.

Case 3 - 10 distinct digits. Same as Case 2.

So the worst case scenario for our "testing machine" will be

8 digits testing - No joy!
9 digits testing - No joy!
10 digits testing - exactly the last one tested turns out to be the match.

Bunuel Please see.

I may be overthinking too much about this! :P :)
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Re: A password to a certain database consists of digits that can [#permalink]

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New post 28 Jul 2017, 06:15
Bunuel wrote:
sumana wrote:
Quote:
Hi, and welcome to the Gmat Club. Below is the solution for your problem.

Total # of passwords possible is \(P^8_{10}=10*9*8*7*6*5*4*3\) (picking 8 different digits out of ten when order of the digits matters, or another approach 10 choices for the 1st digit, 9 choices for the second and so on), 1/5 minute (12 seconds) for one combination, means that time needed to guarantee access to database is \(\frac{P^8_{10}}{5}\) minute.

Hope it's clear

Thank you - But the answer choices are as follows -

a) 8!/5 b) 8!/2 c) 8! d) 10!/2 and e) 5/2.10!


Quote:

Answer to the question you've posted is \(\frac{P^8_{10}}{5}\), which can also be written as \(\frac{10!}{10}=9!\). But still no match with any of the answer choices. Pleas check the question (maybe some info from the stem is missing) or site the source.



Source is Veritas material

I did check the question and following info is missing - If the password is known to consist of at least 8 digits - "at least" is missing


I see. This "at least" changes everything, it means that password can have 8, 9 or 10 digits (more than 10 is not possible as per stem digits must be distinct).

Total # of passwords possible for 8 digits is \(P^8_{10}=\frac{10!}{2}\);
Total # of passwords possible for 9 digits is \(P^9_{10}=10!\);
Total # of passwords possible for 10 digits is \(P^{10}_{10}=10!\).

Time needed to guarantee access to database is \((\frac{10!}{2}+10!+10!)*\frac{1}{5}=\frac{10!}{2}\) minutes.

Answer: D.



But as we need to solve a certain password should not we take the no. of highest possibility that is 10! ??!!!! Plz explain

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Re: A password to a certain database consists of digits that can   [#permalink] 28 Jul 2017, 06:15
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