GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 24 Sep 2018, 08:35

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

9 basketball players are trying out to be on a newly formed

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

Hide Tags

Manager
Manager
avatar
Affiliations: CFA Level 2 Candidate
Joined: 29 Jun 2009
Posts: 197
Schools: RD 2: Darden Class of 2012
9 basketball players are trying out to be on a newly formed  [#permalink]

Show Tags

New post Updated on: 28 Jul 2014, 00:11
4
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

79% (01:00) correct 21% (00:54) wrong based on 284 sessions

HideShow timer Statistics

9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen?

A. 23
B. 30
C. 42
D. 60
E. 126

Originally posted by hogann on 13 Oct 2009, 06:28.
Last edited by Bunuel on 28 Jul 2014, 00:11, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Senior Manager
Senior Manager
User avatar
Affiliations: PMP
Joined: 13 Oct 2009
Posts: 270
Re: 9 basketball players are trying out to be on a newly formed  [#permalink]

Show Tags

New post 13 Oct 2009, 10:07
1
Agree on 60 , 6C3 * 3C2
_________________

Thanks, Sri
-------------------------------
keep uppp...ing the tempo...

Press +1 Kudos, if you think my post gave u a tiny tip

Senior Manager
Senior Manager
User avatar
Joined: 18 Jun 2010
Posts: 275
Schools: Chicago Booth Class of 2013
Reviews Badge
Re: 9 basketball players are trying out to be on a newly formed  [#permalink]

Show Tags

New post 18 Aug 2010, 13:17
How do you get 6C3 * 3C2 ... ?
Manager
Manager
avatar
Status: Last few days....Have pressed the throttle
Joined: 20 Jun 2010
Posts: 63
WE 1: 6 years - Consulting
Re: 9 basketball players are trying out to be on a newly formed  [#permalink]

Show Tags

New post 19 Aug 2010, 02:59
Financier wrote:
How do you get 6C3 * 3C2 ... ?


Out of 6 gaurds we have to select 3 -> selection means we use C -> so 6C3

Out of 3 forwards we have to select 2 -> selection means we use C -> so 3C2

Total ways = 6C3 x 3C2 = 60

Hope this helps!
_________________

Consider giving Kudos if my post helps in some way

Manager
Manager
avatar
S
Joined: 20 Apr 2010
Posts: 223
Location: Hyderabad
WE 1: 4.6 years Exp IT prof
Reviews Badge
Re: 9 basketball players are trying out to be on a newly formed  [#permalink]

Show Tags

New post 21 Aug 2010, 16:53
2
1
Ok answer is 6C3 * 3C2

lets solve this question as
You have 6 positions and you need to place 3 people on that positions
How many ways you can do that
6C3 ways

Similarly you have 3 positions and you want 2 people to take that position in how many ways they can do that
3C2 ways

and they are mutually exclusive events i.e. there is no dependency of selection of guards on selection of forwards and vice versa
hence they should multiply

Therefore ,it is 6C3 * 3C2

I hope it helps let me know if it does if it does not you can always PM me.....!!!!
and don't forget to give a Kudos if you like the explanation....:-)
_________________

I will give a Fight till the End

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."
- Bernard Edmonds

A person who is afraid of Failure can never succeed -- Amneet Padda

Don't Forget to give the KUDOS

Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1868
Re: Help! Comb  [#permalink]

Show Tags

New post 25 Feb 2011, 08:54
3
9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen?
a) 23
b) 30
c) 42
d) 60
e) 126

Sol:
3 guards of 6 guards AND 2 forwards of 3 forwards

\(C^6_3*C^3_2\)
\(\frac{6!}{3!3!}*\frac{3!}{2!1!}\)
\(\frac{6*5*4}{3*2}*\frac{3*2}{2}=60\)

Ans: "d"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
User avatar
Joined: 03 Sep 2010
Posts: 65
Location: Israel
GMAT 1: 660 Q47 V34
GMAT 2: 670 Q48 V34
GPA: 3.2
WE: Operations (Non-Profit and Government)
Re: Help! Comb  [#permalink]

Show Tags

New post 25 Feb 2011, 09:04
1
D. 60.
Choose 3 guards out of 6 * choose 2 forwards out of 3.
(6!/(3!*3!)) * (3!/(2!*1!) = 20 *3 = 60.
Manager
Manager
User avatar
Joined: 17 Feb 2011
Posts: 151
Concentration: Real Estate, Finance
Schools: MIT (Sloan) - Class of 2014
GMAT 1: 760 Q50 V44
Re: Help! Comb  [#permalink]

Show Tags

New post 25 Feb 2011, 09:28
1
You have to proceed with 2 separate combinations:

6C3, which is the number of ways in which you can select 3 guards out of 6. This yields 20
3C2, which is the number of ways in which you can pick 2 forwards out of 3. This yields 3.

Multiply both and you get 60. Answer: D
Intern
Intern
avatar
Joined: 23 Sep 2014
Posts: 14
Re: 9 basketball players are trying out to be on a newly formed  [#permalink]

Show Tags

New post 12 Dec 2014, 05:10
Hi guys,

just wondering if anyone could help me out with how to know whether the order matters. At first i thought it was just 6*5*4 times 3*2. I've been through a course and even with that i find it difficult to know when to apply combinations or permutations. Anyone have clear advice on this? Thanks in advance!
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12443
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: 9 basketball players are trying out to be on a newly formed  [#permalink]

Show Tags

New post 08 Mar 2018, 21:09
Hi All,

This question does NOT ask us to put players "in order", it asks us for groups of players. That clue points to using the Combination Formula. This question has 2 types of players though (guards and forwards), so we have to use the Combination Formula twice (once for each type of player), then multiply the results.

Guards:
There are 6 guards and we're asked for sets of 3.

6c3 = 6!/(3!3!) = 6(5)(4)(3)(2)(1)/3(2)(1)(3)(2)(1) = 20 different sets of 3 guards

Forwards:
There are 3 forwards and we're asked for groups of 2.

3c2 = 3!/(2!1!) = 3(2)(1)/(2)(1)(1) = 3 different groups of 2 forwards

(20)(3) = 60 possible teams

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: 9 basketball players are trying out to be on a newly formed  [#permalink]

Show Tags

New post 12 Mar 2018, 16:34
hogann wrote:
9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen?

A. 23
B. 30
C. 42
D. 60
E. 126


The guards can be chosen in the following number of ways:

6C3 = 6!/[(3!(6 - 3)!] = 6!/)3!3!) = (6 x 5 x 4)/3! = (6 x 5 x 4)/(3 x 2 x 1) = 20 ways

The forwards can be selected in the following number of ways:

3C2 = (3 x 2)/2! = 3 ways

We can pair up each of the 20 ways of choosing guards with each of the 3 ways of choosing forwards. So the total number of teams of 3 guards and 2 forwards is 20 x 3 = 60.

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 2892
Location: Canada
Re: 9 basketball players are trying out to be on a newly formed  [#permalink]

Show Tags

New post 21 Apr 2018, 07:23
Top Contributor
hogann wrote:
9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen?

A. 23
B. 30
C. 42
D. 60
E. 126


Take the task of creating a team and break it into stages.

Stage 1: Select 3 guards from the 6 eligible guards
Since the order in which we select the guards does not matter, we can use combinations.
We can select 3 guards from the 6 eligible guards in 6C3 ways (= 20 ways)
So, we can complete stage 1 in 20 ways

ASIDE: We have a video on calculating combinations (like 6C3) in your head (see below)

Stage 2: Select 2 forwards from the 3 eligible forwards
Since the order in which we select the forwards does not matter, we can use combinations.
We can select 2 forwards from the 3 eligible forwards in 3C2 ways (= 3 ways)
So, we can complete stage 2 in 3 ways

By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus create a basketball team) in (20)(3) ways (= 60 ways)

Answer: D

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

RELATED VIDEOS



_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

GMAT Club Bot
Re: 9 basketball players are trying out to be on a newly formed &nbs [#permalink] 21 Apr 2018, 07:23
Display posts from previous: Sort by

9 basketball players are trying out to be on a newly formed

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.