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

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

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19 Oct 2017, 05:05
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Difficulty:

85% (hard)

Question Stats:

40% (01:47) correct 60% (01:29) wrong based on 70 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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email: nkmungila@gmail.com
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Re: An enterprise has four departments. There are three managers in each  [#permalink]

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19 Oct 2017, 07:03
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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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An enterprise has four departments. There are three managers in each  [#permalink]

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22 Dec 2018, 10:01
chetan2u wrote:
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. $$11!$$

Shouldn't the answer be (6^5)/2 as there is no difference between clockwise and anticlockwise seating?
Consider the similar case of a necklace.
An enterprise has four departments. There are three managers in each &nbs [#permalink] 22 Dec 2018, 10:01
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