It is currently 21 Nov 2017, 22:47

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Private Benjamin is a member of a squad of 10 soldiers, which must vol

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

Hide Tags

Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 889

Kudos [?]: 1869 [0], given: 302

Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User Premium Member
Private Benjamin is a member of a squad of 10 soldiers, which must vol [#permalink]

Show Tags

New post 13 Jul 2015, 12:14
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

78% (01:33) correct 23% (01:15) wrong based on 80 sessions

HideShow timer Statistics

Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability that private Benjamin will be chosen for latrine duty?

A. 1/10
B. 1/5
C. 2/5
D. 3/5
E. 4/5
[Reveal] Spoiler: OA

_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Kudos [?]: 1869 [0], given: 302

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42281

Kudos [?]: 132992 [0], given: 12402

Re: Private Benjamin is a member of a squad of 10 soldiers, which must vol [#permalink]

Show Tags

New post 13 Jul 2015, 12:19
Expert's post
1
This post was
BOOKMARKED
reto wrote:
Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability that private Benjamin will be chosen for latrine duty?

A. 1/10
B. 1/5
C. 2/5
D. 3/5
E. 4/5


Direct approach:

\(\frac{C^1_1*C^3_9}{C^4_{10}}=\frac{2}{5}\).

Reverse approach:

1 - (the probability of 4-member groups without Benjamin) = \(1 -\frac{C^4_9}{C^4_{10}}=\frac{2}{5}\).

Answer: C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132992 [0], given: 12402

Current Student
avatar
B
Joined: 20 Mar 2014
Posts: 2676

Kudos [?]: 1775 [0], given: 794

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: Private Benjamin is a member of a squad of 10 soldiers, which must vol [#permalink]

Show Tags

New post 13 Jul 2015, 12:30
reto wrote:
Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability that private Benjamin will be chosen for latrine duty?

A. 1/10
B. 1/5
C. 2/5
D. 3/5
E. 4/5


Easier way : Desired probability = 1- 'excluded' probability

In this case, Excluded probability = probability of Benjamin not being a part of the 4 volunteers. We can choose 4 out of 9 remaining soldiers in 9C4 ways. total ways possible = 10C4.

Thus excluded probability = 9C4/10C4 = 3/5

Thus, the desired probability = 1- 3/5 = 2/5. Thus C is the correct answer.

Kudos [?]: 1775 [0], given: 794

Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 889

Kudos [?]: 1869 [0], given: 302

Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User Premium Member
Re: Private Benjamin is a member of a squad of 10 soldiers, which must vol [#permalink]

Show Tags

New post 13 Jul 2015, 12:37
Bunuel wrote:
reto wrote:
Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability that private Benjamin will be chosen for latrine duty?

A. 1/10
B. 1/5
C. 2/5
D. 3/5
E. 4/5


Direct approach:

\(\frac{C^1_1*C^3_9}{C^4_{10}}=\frac{2}{5}\).

Reverse approach:

1 - (the probability of 4-member groups without Benjamin) = \(1 -\frac{C^4_9}{C^4_{10}}=\frac{2}{5}\).

Answer: C.


Is there a simple way to reduce \(\frac{C^1_1*C^3_9}{C^4_{10}}\) to 2/5 or do you also have to split it up to 9*8*7/3*2*1 / 210 and then go from there...?
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Kudos [?]: 1869 [0], given: 302

1 KUDOS received
Current Student
avatar
B
Joined: 20 Mar 2014
Posts: 2676

Kudos [?]: 1775 [1], given: 794

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Private Benjamin is a member of a squad of 10 soldiers, which must vol [#permalink]

Show Tags

New post 13 Jul 2015, 12:45
1
This post received
KUDOS
reto wrote:
Bunuel wrote:
reto wrote:
Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability that private Benjamin will be chosen for latrine duty?

A. 1/10
B. 1/5
C. 2/5
D. 3/5
E. 4/5


Direct approach:

\(\frac{C^1_1*C^3_9}{C^4_{10}}=\frac{2}{5}\).

Reverse approach:

1 - (the probability of 4-member groups without Benjamin) = \(1 -\frac{C^4_9}{C^4_{10}}=\frac{2}{5}\).

Answer: C.


Is there a simple way to reduce \(\frac{C^1_1*C^3_9}{C^4_{10}}\) to 2/5 or do you also have to split it up to 9*8*7/3*2*1 / 210 and then go from there...?


you can look it at like this:

Remove Benjamin from the equation for now. You have 10 people from which only 9 are applicable to choose 4 volunteers from.

Thus the probabilities of selecting 1st,2nd , 3rd and 4th volunteers will be : (9/10) [you have 9 favorable choices out of 10 available], (8/9)[you have 8 favorable choices out of 9 available], (7/8)[you have 7 favorable choices out of 8 available], (6/7)[you have 6 favorable choices out of 17 available] .

The final probability (without Benjamin) will be (9/10)*(8/9)*(7/8)*(6/7) = 3/5.

Thus the Probability with Benjamin selected = 1-3/5 = 2/5.

As far as reducing nCr is concerned, there is only 1 formula: nCr = n!/ [r!*(n-r)!)]

Kudos [?]: 1775 [1], given: 794

Manager
Manager
User avatar
S
Joined: 31 May 2015
Posts: 70

Kudos [?]: 32 [0], given: 117

GMAT ToolKit User
Re: Private Benjamin is a member of a squad of 10 soldiers, which must vol [#permalink]

Show Tags

New post 01 Jun 2016, 12:00
If we assume that Benjamin is volunteering to be on the 4 group can we derive 4/10 =2/5 no??
_________________

GMAT loosers are born not made !!!

Kudos [?]: 32 [0], given: 117

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15562

Kudos [?]: 283 [0], given: 0

Premium Member
Re: Private Benjamin is a member of a squad of 10 soldiers, which must vol [#permalink]

Show Tags

New post 09 Oct 2017, 09:21
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1684

Kudos [?]: 910 [0], given: 5

Re: Private Benjamin is a member of a squad of 10 soldiers, which must vol [#permalink]

Show Tags

New post 12 Oct 2017, 18:03
reto wrote:
Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability that private Benjamin will be chosen for latrine duty?

A. 1/10
B. 1/5
C. 2/5
D. 3/5
E. 4/5


The number of ways 4 people can be chosen from 10 is 10C4 = 10!/[4!(10-4)!] = (10 x 9 x 8 x 7)/(4 x 3 x 2 x 1) = 10 x 3 x 7.

If Private Benjamin must be 1 of the 4 people chosen, then we have to choose 3 people from the remaining 9 people. The number of ways 3 people can be chosen from 9 is 9C3 = 9!/[3!(9-3)!] = (9 x 8 x 7)/(3 x 2 x 1) = 3 x 4 x 7.

Thus, the probability that Private Benjamin will be chosen for latrine duty is:

9C3/10C4 = (3 x 4 x 7)/(10 x 3 x 7) = 4/10 = 2/5

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

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

Kudos [?]: 910 [0], given: 5

Re: Private Benjamin is a member of a squad of 10 soldiers, which must vol   [#permalink] 12 Oct 2017, 18:03
Display posts from previous: Sort by

Private Benjamin is a member of a squad of 10 soldiers, which must vol

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.