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# An enterprise has four departments. There are three managers in each

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Manager
Joined: 07 Jun 2017
Posts: 174
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
An enterprise has four departments. There are three managers in each  [#permalink]

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19 Oct 2017, 06:05
5
00:00

Difficulty:

55% (hard)

Question Stats:

50% (02:03) correct 50% (02:13) wrong based on 43 sessions

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An enterprise has four departments. There are three managers in each of the four departments. These managers are to be
seated along a circular table in such a way that all managers from the same department sit together. Two arrangements are
considered different only when the neighbours of any manager change. How many different arrangements of seating are
possible?

A. $$144$$

B. $$488$$

C. $$6^5$$

D. $$\frac{11!}{(3!)^4}$$

E. $$11!$$

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Naveen
email: nkmungila@gmail.com
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Joined: 02 Aug 2009
Posts: 6959
Re: An enterprise has four departments. There are three managers in each  [#permalink]

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19 Oct 2017, 08:03
nkmungila wrote:
An enterprise has four departments. There are three managers in each of the four departments. These managers are to be
seated along a circular table in such a way that all managers from the same department sit together. Two arrangements are
considered different only when the neighbours of any manager change. How many different arrangements of seating are
possible?

A. $$144$$

B. $$488$$

C. $$6^5$$

D. $$\frac{11!}{(3!)^4}$$

E. $$11!$$

Hi..
Four departments and each has three managers, so managers in each can be seated in 3! Ways, so for all 4 depts, 3!*3!*3!*3!...
These four departments are arranged in circular table and can be arranged in (4-1)!=3!...

Total ways = 3!*3!*3!*3!*3!=6^5

C
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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

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Re: An enterprise has four departments. There are three managers in each &nbs [#permalink] 19 Oct 2017, 08:03
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