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Probability

by tanvis1120 » Thu Jan 30, 2014 4:33 pm
From a group of N employees, K will be selected, at random, to sit in a line of K chairs. There are absolutely no restrictions, either in the selection process nor in the order of seating. What is the probability that the employee Dave is seated exactly next to employee Bill?

Statement 1: K=20
Statement 2: K=N
Last edited by tanvis1120 on Thu Jan 30, 2014 4:44 pm, edited 1 time in total.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Thu Jan 30, 2014 4:38 pm
tanvis1120 wrote:From a group of N employees, K will be selected, at random, to sit in a line of K chairs. There are absolutely no restrictions, either in the selection process nor in the order of seating. What is the probability that the employee Dave is seated exactly next to employee Bill?
Is this a Data Sufficiency question?
If so, please provide the two statements.
If it's a Problem Solving question, please provide the answer choices.

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by tanvis1120 » Thu Jan 30, 2014 4:45 pm
Updated !
I am sorry.. It was my bad.

Thanks Brent..
If you could please explain the solution to me...
Help Appreciated !
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by [email protected] » Fri Jan 31, 2014 12:08 am
Hi tanvis1120,

This DS question is more of a "concept" question than a "math" question, so you don't really need to do any math to solve it (you just need to understand what the math would be and if you have enough information to do that math).

We're told there are N employees and K will be selected to sit in a row of K chairs. We're asked what the probability would be that Dave would sit next to Bill? Since we don't know the number of employees, nor the number of chairs, there's a big "hole" in the information. We'll need some specifics to answer the question.

Fact 1: K = 20

Now we know that there are 20 chairs, but we have no way of knowing if Dave and Bill will even be selected from the total number of employees. Maybe just one of them will or maybe neither of them will. There's no way to calculate the answer with just this info.
Fact 1 is INSUFFICIENT.

Fact 2: K = N

Now we know that every employee will be selected, but we still don't know what the probability is that Dave and Bill will sit next to each other.

If K = N = 2, then Dave and Bill are the only employees and there's a 100% probability that they sit next to one another.
If K = N = ANYTHING > 2, then Dave and Bill might not sit next to each other, so the probability is less than 100%
Fact 2 is INSUFFICIENT

Combined, we know that there are 20 employees and that they all get seated. From here, you COULD calculate the probability of Dave sitting next to Bill. The good part is that you don't have to do that math to answer this question.
Combined, SUFFICIENT.

Final Answer: C

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by sanju09 » Fri Jan 31, 2014 3:18 am
tanvis1120 wrote:From a group of N employees, K will be selected, at random, to sit in a line of K chairs. There are absolutely no restrictions, either in the selection process nor in the order of seating. What is the probability that the employee Dave is seated exactly next to employee Bill?

Statement 1: K=20
Statement 2: K=N
Statement (1) is insufficient as the value of N is not Known.

Statement (2) has an important point to ponder, which is 'selecting all', that means only one way of selection.

Total number of ways in which K employees can be made to sit on K chairs = K!

If two of them were to sit together, then let's get them out from K first leaving K - 2 employees, next take this pair as one body which can be arranged in 2! number of ways, next add this one body to K - 2 employees,

making the favorable number of arrangements = 2! (k - 1)!

Thus the required probability = 2! (k - 1)!/K! = 2/K. We don't know the value of K. Insufficient

From (1) K = 20, hence the required probability = [spoiler]2/20 = 1/10. Sufficient

Pick C[/spoiler]
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