At a dinner party, 5 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total nummber of different possible seating arrangements for the group?
(A) 5
(B) 10
(C) 24
(D) 32
(E) 120
(E) 120
C
(C) 24
B-10
A
As position diff relative to each other so everyone will be besides everyone else once
so 5
Take GMAT team, please provide the answer.
Come friends, the question is just asking us the number of arrangements of 5 people around a circular table.
Do not get misled by the extra wordings !!
The extra wordings are intended only to tell us that this is a “Permutation” problem rather than a “Combination” one.
Answer is -
(n-1)! = 4! = 24.
C
HTH
~magnus1
can someone please provide the correct answer?
i got 120
The answer should be (5-1)! = 4! = 24
So (C)
Same as the different ways in which 5 people can be arranged in a straight line… A-B-C-D-E ::: However the case of relative posiutions deems that BCDEA is the same as ABCDE …Thus its the same as fixing a single person and moving the rest 4 around him/her
thus 4 ! = 24
Ans is C =24
(5-1)! = 4! = 24 Different arrangements
Regards
A.c.
C
The answer is C.
It´s a Circular Permutations question.
C
perhaps this link could clarify something.
http://tutors4you.com/circularpermutations.htm
I think C (24) is correct
120 is the answer acc. to me.
let there be five persons p1 … p5
and the chairs be c1…c5
keep p1 in c1 and shuffle others you will get 24 (4*3*2) combinations possible.
similarly for each persons p2 to p5 seated in c1 there are 24 combinations each
so u get 5 * (4!) = 5*24 = 120 or you could simply say 5!.
Pls let me know is this is wrong
Ans is E
because
the 1st position can be taken by any of then means 5
now the 1st person already have seat so the 2nd can be taken by 4 persons
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means like that
the total no. of combinations will be 5x4x3x2x1 = 120
acc to me the ans is 120(E).this is a permutation question bcoz the order matters(as the position of people are different relative to each other for each arrangement).hence 5! that is 120.
Thanks, thiago, for the link — very helpful.
the online “tutor” states that if rotations don’t count as original permutations, then the total # of circular permutations equals (n-1)!/2!. this question’s emphasis on where guests are seated relative to one another suggests that we’re dealing with such a problem.
so:
(5-1)!/2!
4!/2!
12 … which, of course, isn’t an option.
take gmat team, am i misinterpreting the question? applying the wrong formula? both?
thanks.
the answer is 24
if there are n objects one circular permutation corresponds to
of these objects correspond to n linear arrangements as
a1,a2,a3…..an
a2,a3,a4…an,a1
….until an,,…a1.these n arrangements correspond to only 1 circular permutation as in the case of the latter difference in arrangement is only becoz of change in relative position.
let x be the number of circular permutations
x*n=n!(the total number of arrangements of n objects)
x=(n-1)!
in this question 5 is the number of people hence number of cicular arrangements=4!=24
B
C) 24
Let’s name guests A,B,C,D & E
Assume that Guest A’s place does not change at the table and always is sitting is the first spot. There are six combinations with guest B sitting to her left:
ABCDE
ABCED
ABDCE
ABDEC
ABECD
ABEDC
There will be an additional six combinations for each guest. Therfore:
4 X 6 = 24 (C)
Answer is C.. 24..
C 24
answer is C…24
If clockwise and anti clock-wise orders are different, then total number of circular-permutations is given by (n-1)!
therefore, (5-1)! = 24
ans is C
if 5 people are to be seated in a straight row the the answer will be 5! that is 120, HOWEVER if there is a round sitting arrangement then we have to fix 1 person as base and rest 4 revolves around him so ans is (5-1)! that is 24.
i think the answer is C.if we fix 1 person then the other 4 can sit in 4! ways.which is 24.option C.
C is the one!
24
circular permutations (n-1)! … its simplest of question .. so ans 24 …
Umm, no, this is not a circular permutation problem. Neither clockwise nor counterclockwise rotations count as distinct seating arrangements. It is a “linear” permutation problem, so 5! is the answer (E).
thanks thiago, that was really useful!
the answer is (n-1)!=(5-1)!=4!=4x3x2x1=24
24 is the answer
I don’t know why…