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

It is currently 16 Dec 2018, 03:36

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 in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.
  • Free GMAT Prep Hour

     December 16, 2018

     December 16, 2018

     03:00 PM EST

     04:00 PM EST

    Strategies and techniques for approaching featured GMAT topics

During a war a Major is supposed to send 5 units of soldiers to 5 diff

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

Hide Tags

Intern
Intern
avatar
S
Joined: 21 May 2016
Posts: 27
GMAT ToolKit User Premium Member CAT Tests
During a war a Major is supposed to send 5 units of soldiers to 5 diff  [#permalink]

Show Tags

New post 28 Sep 2018, 08:56
3
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

38% (01:06) correct 62% (02:04) wrong based on 39 sessions

HideShow timer Statistics

During a war a Major is supposed to send 5 units of soldiers to 5 different borders. If he has 30 soldiers and has to send an equal number of soldiers to 5 regions, in how many ways can he do so?

A. \(30!/(5!)^6\)

B. \(30!/(5!)^5\)

C. \(30!/(6!)^5\)

D. \((30!/6!^5)5!\)

E. \(30!/(6!^5*5!)\)

_________________

If you like my post press +1 Kudos

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7108
Re: During a war a Major is supposed to send 5 units of soldiers to 5 diff  [#permalink]

Show Tags

New post 28 Sep 2018, 09:50
2
3
a70 wrote:
During a war a Major is supposed to send 5 units of soldiers to 5 different borders. If he has 30 soldiers and has to send an equal number of soldiers to 5 regions, in how many ways can he do so?

A. \(30!/(5!)^6\)

B. \(30!/(5!)^5\)

C. \(30!/(6!)^5\)

D. \((30!/6!^5)5!\)

E. \(30!/(6!^5*5!)\)



Straight formula ..
If you have to make 5 groups of 6 people from (5*6) people, answer is \(\frac{(5*6)!}{(6!)^5}\)

Now if you do not know the formula..
First 6 can be selected in 30C6
Next 6 from remaining 24 in 24C6 and so on
So 30C6*24C6*18C6*12C6*6C6
\(\frac{30!}{24!6!}*\frac{24!}{18!6!}*\frac{18!}{12!6!}*\frac{12!}{6!6!}*\frac{6!}{0!6!}=\frac{30!}{6!6!6!6!6!}=\frac{30!}{(6!)^5}\)

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

General Discussion
Director
Director
User avatar
P
Joined: 14 Dec 2017
Posts: 518
Location: India
Premium Member
Re: During a war a Major is supposed to send 5 units of soldiers to 5 diff  [#permalink]

Show Tags

New post 30 Sep 2018, 08:14
a70 wrote:
During a war a Major is supposed to send 5 units of soldiers to 5 different borders. If he has 30 soldiers and has to send an equal number of soldiers to 5 regions, in how many ways can he do so?

A. \(30!/(5!)^6\)

B. \(30!/(5!)^5\)

C. \(30!/(6!)^5\)

D. \((30!/6!^5)5!\)

E. \(30!/(6!^5*5!)\)



Using the concept, if 2n different items are to divided into 2 groups of n items each, then it can be done in \(\frac{(2n)!}{{n!*n!*2!}}\)

Here we have 30 soldiers, hence 5*6 items to be divided into 5 groups of 6 items each.

30 soldiers can be divided into 5 units of 6 soldiers each in \(\frac{30!}{((6!)^{5}*5!)}\)

The 5 units can then be sent to the 5 different borders in 5! ways.

Hence total # of ways of doing this is = \(\frac{30!}{((6!)^{5}*5!)}*5!\) = \(30!/(6!)^5\)


Answer C.


Thanks,
GyM
_________________

New to GMAT Club - https://gmatclub.com/forum/new-to-gmat-club-need-help-271131.html#p2098335

GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 544
During a war a Major is supposed to send 5 units of soldiers to 5 diff  [#permalink]

Show Tags

New post 30 Sep 2018, 08:42
Quote:
During a war a Major is supposed to send 5 units of 6 soldiers in each unit to 5 different borders. Into how many groups the 30 soldiers may be divided?

A. \(30!/(5!)^6\)

B. \(30!/(5!)^5\)

C. \(30!/(6!)^5\)

D. \((30!/6!^5)5!\)

E. \(30!/(6!^5*5!)\)

[In the original question stem, we could send (say) just 5 soldiers -one to each border - from the 30 soldiers available, without violating the restrictions imposed.]

\(?\,\,:\,\,\,\# \,\,{\rm{groups}}\)

Border A: C(30,6) choices
Border B: C(24,6) choices
Border C: C(18,6) choices
Border D: C(12, 6) choices
Border E: C(6,6) choices or, if you prefer, the soldiers left ("no choices" then).

Using the Multiplicative Principle, we have:

\(?\,\,\, = \,\,\,\left( {{{30!} \over {6!\,\,24!}}} \right)\,\,\left( {{{24!} \over {6!\,\,18!}}} \right)\left( {{{18!} \over {6!\,\,12!}}} \right)\,\,\left( {{{12!} \over {6!\,\,6!}}} \right)\,\,\, = \,\,\,{{30!} \over {{{\left( {6!} \right)}^5}}}\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

GMAT Club Bot
During a war a Major is supposed to send 5 units of soldiers to 5 diff &nbs [#permalink] 30 Sep 2018, 08:42
Display posts from previous: Sort by

During a war a Major is supposed to send 5 units of soldiers to 5 diff

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


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®.