Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

The Competition Continues - Game of Timers is a team-based competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th

Joe is among N people in a group, where N > 3. If 3 people are randoml
[#permalink]

Show Tags

14 May 2019, 13:01

2

Top Contributor

4

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

63% (02:24) correct 37% (02:41) wrong based on 82 sessions

HideShow timer Statistics

Joe is in a group consisting of N people (N > 4). If 3 people from the group are randomly selected to be on a committee, what is the probability that Joe is selected?

Joe is among N people in a group, where N > 3. If 3 people are randoml
[#permalink]

Show Tags

Updated on: 15 May 2019, 09:06

6

1

There are two easy ways to solve this question.

First is what gmatkarma20 explained in the first post. The benefit of this method is that you can solve by taking any value of N and get the same answer.

The other is to solve in terms of N. First, total number of cases in which we can select 3 people from N people is: C(n,3) or nC3 N*(N-1)*(N-2)/3*2*1

If Joe has to be in the team, we need to select only 2 more people from the remaining ‘N-1’ people. This can be done in: (n-1)C2 or C(n-1,2) (N-1)*(N-2)/2*1

The extra effort that you have to take when substituting values is to check all options and eliminate the ones that will not end with the desired answer.

Re: Joe is among N people in a group, where N > 3. If 3 people are randoml
[#permalink]

Show Tags

15 May 2019, 09:22

Top Contributor

Vinit800HBS wrote:

There are two easy ways to solve this question.

First is what gmatkarma20 explained in the first post. The benefit of this method is that you can solve by taking any value of N and get the same answer.

The other is to solve in terms of N. First, total number of cases in which we can select 3 people from N people is: C(n,3) or nC3 N*(N-1)*(N-2)/3*2*1

If Joe has to be in the team, we need to select only 2 more people from the remaining ‘N-1’ people. This can be done in: (n-1)C2 or C(n-1,2) (N-1)*(N-2)/2*1

Joe is among N people in a group, where N > 3. If 3 people are randoml
[#permalink]

Show Tags

Updated on: 16 May 2019, 06:13

1

Top Contributor

GMATPrepNow wrote:

Joe is in a group consisting of N people (N > 4). If 3 people from the group are randomly selected to be on a committee, what is the probability that Joe is selected?

A) \(\frac{N^2-2N-6}{(N-2)^2+6}\)

B) \(\frac{2N+3}{N^2-N}\)

C) \(\frac{3}{N}\)

D) \(\frac{N}{(N-1)(N-2)}\)

E) \(\frac{N^2-1}{5N}\)

My solution:

If there are N people, then we can select 3 people in NC3 (N choose 3) different ways. NC3 = \(\frac{(N)(N-1)(N-2)}{3!}\) = \(\frac{(N)(N-1)(N-2)}{6}\) So, this is our denominator

In how many of the (N)(N-1)(N-2)/6 possible outcomes is Joe chosen? Well, once we make Joe one of the selected people, there are N-1 people remaining. We can select 2 people from the remaining N-1 people in (N-1)C2 ways (N-1)C2 = \(\frac{(N-1)(N-2)}{2!}\) = \(\frac{(N-1)(N-2)}{2}\) This is our numerator

So, P(Joe is selected) = \(\frac{(N-1)(N-2)}{2}\) ÷ \(\frac{(N)(N-1)(N-2)}{6}\)

= \(\frac{(N-1)(N-2)}{2}\) x \(\frac{6}{(N)(N-1)(N-2)}\)

That's sound advice. However, I believe Render was saying that, once we know the correct answer is A or C, we can quickly eliminate A by testing N = 10 Although it's ideal to eliminate 4 of the 5 answer choices in the first round, Render's approach helps us quickly arrive at the correct answer.

I'm not able to understand the concept behind your approach. I think in the problem as follows:

Probability to choose Joe = (choose Joe from from N persons) * (choose 2nd person from N-1 persons) * (choose 3rd person from N-2 persons) + (choose 1st person from N persons) *(choose Joe from from N-1 persons) * (choose 3rd person from N-2 persons) + (choose 1st person from N persons) *(choose 2nd person from N-1 persons) * (choose Joe from from N-2 persons)

I'm not able to understand the concept behind your approach. I think in the problem as follows:

Probability to choose Joe = (choose Joe from from N persons) * (choose 2nd person from N-1 persons) * (choose 3rd person from N-2 persons) + (choose 1st person from N persons) *(choose Joe from from N-1 persons) * (choose 3rd person from N-2 persons) + (choose 1st person from N persons) *(choose 2nd person from N-1 persons) * (choose Joe from from N-2 persons)

Is my approach incorrect?

Thanks in advance

In your approach, you basically saying that order matters That is, you're saying selecting Joe then Al then Bea is different from Al then Joe then Bea

That approach approach will work as long as you treat the denominator the same way. That is, the TOTAL number of ways to select 3 people from N people = (N)(N-1)(N-2)

If you do that, then you should arrive at the correct answer.

Re: Joe is among N people in a group, where N > 3. If 3 people are randoml
[#permalink]

Show Tags

16 May 2019, 13:05

GMATPrepNow wrote:

GMATPrepNow wrote:

Joe is in a group consisting of N people (N > 4). If 3 people from the group are randomly selected to be on a committee, what is the probability that Joe is selected?

A) \(\frac{N^2-2N-6}{(N-2)^2+6}\)

B) \(\frac{2N+3}{N^2-N}\)

C) \(\frac{3}{N}\)

D) \(\frac{N}{(N-1)(N-2)}\)

E) \(\frac{N^2-1}{5N}\)

My solution:

If there are N people, then we can select 3 people in NC3 (N choose 3) different ways. NC3 = \(\frac{(N)(N-1)(N-2)}{3!}\) = \(\frac{(N)(N-1)(N-2)}{6}\) So, this is our denominator

In how many of the (N)(N-1)(N-2)/6 possible outcomes is Joe chosen? Well, once we make Joe one of the selected people, there are N-1 people remaining. We can select 2 people from the remaining N-1 people in (N-1)C2 ways (N-1)C2 = \(\frac{(N-1)(N-2)}{2!}\) = \(\frac{(N-1)(N-2)}{2}\) This is our numerator

So, P(Joe is selected) = \(\frac{(N-1)(N-2)}{2}\) ÷ \(\frac{(N)(N-1)(N-2)}{6}\)

= \(\frac{(N-1)(N-2)}{2}\) x \(\frac{6}{(N)(N-1)(N-2)}\)

= \(\frac{6(N-1)(N-2)}{2(N)(N-1)(N-2)}\)

= \(\frac{6}{2N}\)

= \(\frac{3}{N}\)

Answer: C

Cheers, Brent

Dear Brent,

Thanks a lot for your reply. I followed your advice and it yielded the same result.

But I want to understand 2 things in your solution as it is more easier:

1- I used permutation as I think order matters. However, you used combination. why? Does not order matter?

2- In you solution you choose only 2 out of N-1. I do not understand the logic itself. How Joe is included in your solution. I hope you can elaborate.

Re: Joe is among N people in a group, where N > 3. If 3 people are randoml
[#permalink]

Show Tags

17 May 2019, 05:19

1

Top Contributor

Mo2men wrote:

Dear Brent,

Thanks a lot for your reply. I followed your advice and it yielded the same result.

But I want to understand 2 things in your solution as it is more easier:

1- I used permutation as I think order matters. However, you used combination. why? Does not order matter?

2- In you solution you choose only 2 out of N-1. I do not understand the logic itself. How Joe is included in your solution. I hope you can elaborate.

Thanks in advance

1) We can go either way with this (i.e., order matters or order does not matter), as long as you use the same construct for numerator and denominator. In my approach, I'm assuming order does not matter For example, selecting Joe then Al then Bea is the SAME as selecting Al then Joe then Bea

2) To count the number of outcomes where Joe is selected to be on the 3-person committee, I first placed Joe on the committee (which means there are N-1 people left to choose from), and then I selected 2 more people to join Joe on the committee. So, we are selecting 2 people (from N-1 people) to be on the committee with Joe.