John and Peter are among the nine players a basketball coach : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 22 Jan 2017, 11:37

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# John and Peter are among the nine players a basketball coach

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 23 Jun 2005
Posts: 24
Followers: 0

Kudos [?]: 8 [0], given: 0

John and Peter are among the nine players a basketball coach [#permalink]

### Show Tags

17 Aug 2006, 19:41
6
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

72% (02:54) correct 28% (01:55) wrong based on 204 sessions

### HideShow timer Statistics

John and Peter are among the nine players a basketball coach can choose from to field a five-player team. If all five players are chosen at random, what is the probability of choosing a team that includes John and Peter?

a) 1/9
b) 1/6
c) 2/9
d) 5/18
e) 1/3

OPEN DISCUSSION OF THIS QUESTION IS HERE: john-and-peter-are-among-the-nine-players-a-basketball-coach-68186.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Dec 2014, 06:46, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Intern
Joined: 23 Jun 2005
Posts: 24
Followers: 0

Kudos [?]: 8 [1] , given: 0

Re: John and Peter are among the nine players a basketball coach [#permalink]

### Show Tags

17 Aug 2006, 19:48
1
KUDOS
this is what i tried:

find out the probability of not choosing John and Peter

7/9 * 6/8 * 5/7 * 4/6 * 3/5 = 1/6

1 - 1/6 = 5/6

where did i go wrong?
VP
Joined: 25 Jun 2006
Posts: 1172
Followers: 3

Kudos [?]: 148 [1] , given: 0

Re: John and Peter are among the nine players a basketball coach [#permalink]

### Show Tags

17 Aug 2006, 19:57
1
KUDOS
Answer is D: 5/18.

Total possible ways of selecting a 5-member team:
a combination problem, not permutation since order does not matter:

9x8x7x6x5/(5x4x3x2x1) = 126.

The ways of selecting a 5-member team including John and Peter:
It is again a combination, not permutation. Since John and Peter are already included, you don't bother about them any more. The possible ways will be the combination of the rest of the 3 players from the rest of 7 player:
7x6x5/(3x2x1) = 35.

so the probability = 35/126 = 5/18.
Manager
Joined: 09 Jul 2006
Posts: 85
Location: India
Followers: 1

Kudos [?]: 1 [1] , given: 0

Re: John and Peter are among the nine players a basketball coach [#permalink]

### Show Tags

17 Aug 2006, 20:04
1
KUDOS
Dear minhthel,
What you have done is that you have calculated the probability choosing Jon OR Peter OR Jon + Peter (5/6). We need to find the probability only of Jon + Peter.
The way I have done it is:
Total number of combinations possible for a 5 member team from a group of 9 players = 9C5
Total number of combinations possible for a 5 member team consisting of Jon + Peter out of the group of 9 players = 7C3
I got this because out of the 5 slots in the team, 2 have now been fixed. So there are only 3 slots available for the different combinations. Also now the choice needs to be made only amongst 7 players (Jon and Peter already decided).
Hence probability of selecting Jon + Peter in the team = 7C3/9C5 = 5/18.
What is the OA please ?
Any other approaches to solving this kind of problem ?
_________________

Cheers!
Prashrash.

VP
Joined: 02 Jun 2006
Posts: 1267
Followers: 2

Kudos [?]: 80 [0], given: 0

Re: John and Peter are among the nine players a basketball coach [#permalink]

### Show Tags

17 Aug 2006, 20:21
d) 5/18

Picking 5 of 9 = 9x8x7x6x5/5x4x3x2= 126

# of ways to pick John and Peter and 3 others from 9-2 = 7 is :
7x6x5/3x2 = 35

Prob = 35/126 = 5/18
CEO
Joined: 20 Nov 2005
Posts: 2911
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 24

Kudos [?]: 273 [1] , given: 0

Re: John and Peter are among the nine players a basketball coach [#permalink]

### Show Tags

17 Aug 2006, 21:08
1
KUDOS
1
This post was
BOOKMARKED
Total cases = 9C5
cases when these two are selected = 7C3
Prob = 7C3/9C5 = 5/18

Minthel,

If we take your method then it will take hell lot of time.
You have considered only this order:
1st selection NOT one of these two
2nd selection NOT one of these two
3rd selection NOT one of these two
4th selection NOT one of these two
5th selection NOT one of these two

We have to consider two many more cases. X is any other than J and P.
JXXXX
XJXXX
XXJXX
XXXJX
XXXXJ
then 5 more for XXXXP.
It is becoming more complex.

If you still want to solve that way then here I go:

JPXXX how may ways this can be arranged
5!/3! = 20
Take one case JPXXX - 1/9 * 1/8 * 7/7 * 6/6 * 5/5
JXPXX - 1/9 * 7/8 * 1/7 * 6/6 * 5/5

So denominators of all these cases will be 9*8*7*6*5 and numerator will be 1*1*7*6*5

So prob = 20 * 7*6*5/(9*8*7*6*5) = 20/72 = 5/18
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13501
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: John and Peter are among the nine players a basketball coach [#permalink]

### Show Tags

14 Dec 2014, 23:09
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36598
Followers: 7096

Kudos [?]: 93458 [3] , given: 10563

Re: John and Peter are among the nine players a basketball coach [#permalink]

### Show Tags

15 Dec 2014, 06:46
3
KUDOS
Expert's post
7
This post was
BOOKMARKED
John and Peter are among the nine players a basketball coach can choose from to field a five-player team. If all five players are chosen at random, what is the probability of choosing a team that includes John and Peter?
A. 1/9
B. 1/6
C. 2/9
D. 5/18
E. 1/3

Probability approach:
1/9 choosing John (J);
1/8 choosing Peter (P);
7/7=1 choosing any (A) for the third player;
6/6=1 choosing any (A) for the fourth player;
5/5=1 choosing any (A) for the fifth player.

But scenario JPAAA can occur in $$\frac{5!}{3!}=20$$ # of ways (JAPAA, JAAPA, AAAPJ, ... basically the # of permutations of the letters JPAAA, which is $$\frac{5!}{3!}=20$$).

So $$P=\frac{5!}{3!}*\frac{1}{9}*\frac{1}{8}*1*1*1=\frac{5}{18}$$.

Combinatorics approach:

P=favorable outcomes/total # of outcomes --> $$P=\frac{C^2_2*C^3_7}{C^5_9}=\frac{5}{18}$$.

$$C^2_2=1$$ - # of ways to choose Peter and John out of Peter and John, basically 1 way;
$$C^3_7=35$$ - # of ways to choose 3 other players out of 7 players left (without Peter and John);
$$C^5_9=126$$ - total # of ways to choose 5 players out of 9.

OPEN DISCUSSION OF THIS QUESTION IS HERE: john-and-peter-are-among-the-nine-players-a-basketball-coach-68186.html
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13501
Followers: 577

Kudos [?]: 163 [0], given: 0

Re: John and Peter are among the nine players a basketball coach [#permalink]

### Show Tags

01 Apr 2016, 11:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Director
Joined: 21 Jun 2014
Posts: 507
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
Followers: 12

Kudos [?]: 167 [0], given: 92

Re: John and Peter are among the nine players a basketball coach [#permalink]

### Show Tags

09 Apr 2016, 01:06
minhthel wrote:
John and Peter are among the nine players a basketball coach can choose from to field a five-player team. If all five players are chosen at random, what is the probability of choosing a team that includes John and Peter?

a) 1/9
b) 1/6
c) 2/9
d) 5/18
e) 1/3

OPEN DISCUSSION OF THIS QUESTION IS HERE: john-and-peter-are-among-the-nine-players-a-basketball-coach-68186.html

Remember - if it is certain that X HAS TO BE chosen then he can be chosen only in one way. because it is certain.

so we need to choose 3 people from remaining 7 people because John an peter is included.

Probability of choosing a team that includes John and Peter = (1 * 1 * 7C3) / 10C5 = 5/18
_________________

---------------------------------------------------------------
Target - 720-740
helpful post means press '+1' for Kudos!
http://gmatclub.com/forum/information-on-new-gmat-esr-report-beta-221111.html
http://gmatclub.com/forum/list-of-one-year-full-time-mba-programs-222103.html

Re: John and Peter are among the nine players a basketball coach   [#permalink] 09 Apr 2016, 01:06
Similar topics Replies Last post
Similar
Topics:
6 Coach John has to form a team of 4 players to be selected from a pool 5 29 Jan 2015, 07:43
17 A basketball coach will select the members of a five-player 16 07 May 2012, 07:16
1 A basketball coach will select the members of a five-player 5 17 Aug 2010, 10:27
9 basketball players are trying out to be on a newly formed basketball 3 11 Aug 2010, 10:08
58 John and Peter are among the nine players a basketball coach 32 31 Jul 2008, 15:56
Display posts from previous: Sort by

# John and Peter are among the nine players a basketball coach

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.