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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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:

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

Show Tags

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?

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

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

Show Tags

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.

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

Show Tags

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.

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

Show Tags

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)!)]

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

Show Tags

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.
_________________

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