4 managers, 2 vice-presidents and 1 president have to be seated in a c

Question

4 managers, 2 vice-presidents and 1 president have to be seated in a circle for a meeting such
that the two vice-presidents sit on either side of the president. In how many ways can they be
seated?

A. 120

B. 240

C. 36

D. 48

E. 72

chetan2u · Answer

Fix the president in a seat. The adjoining two seats will be for the vp, so 2 ways. 
Remaining 4 seats will be occupied by managers in 4! or 24 ways.

Total: 24*2 or 48 ways.

100mitra · Answer

Correct Option D

1. Number of ways seating arrangements can be done with fix position of president : 1
2. Number of ways all other 6 memeber can be arranged : 6 x 5 x 4 x 3 x 2 x 1 = 720
3. Number of ways 4 manager can be arranged : 4 x 3 x 2 x 1 = 24
4. Number of ways 2 VP can be arranged : 6 x 5 = 30

In fix pattern seating arrangements
 \frac{(1 * 720) }{ (24 * 30) }  = 48

Option D

GMATWhizTeam · Answer

Solution:

We have 4 managers, 2 vice-presidents and 1 president sitting at a circular table.

We are told that two vice-presidents sit on either side of the president. This means we have 2 scenarios there:  VP_1 ,P, VP_2  or  VP_2, P, VP_1

Now let us assume VP, P, VP as a single entity because they will always be together. So we have 5 entities now including 4 managers.

Number of ways in which these 5 entities can sit around a round table  = (5-1)!= 4!=24 . Because we know  number of ways in which n people can sit in circle is  (n-1)!

These 24 arrangements can be done twice. Once in the case of  VP_1 ,P, VP_2  and other in the case of  VP_2 ,P, VP_1 .

So total number of ways  = 2	imes 24 =48 ..

Hence the right answer is    Option D   .

Crytiocanalyst · Answer

let the vice presidents be places between and considering them as a single unit

Therefore total number of people to be arranged in circular permutation = 5 in 4! ways

and the vice presidents can be arranged in 2! ways

Total number of arrangements = 4!*2! = 48 
THerefore IMO D

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4 managers, 2 vice-presidents and 1 president have to be seated in a c

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4 managers, 2 vice-presidents and 1 president have to be seated in a c

Prep Toolkit

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