Fix one person in one place, so the permutations for the remaining 4 will be 4! = 4*3*2*1 = 24
[spoiler]The correct answer is (C).[/spoiler]
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Gmat Prep-Seating arrangement
Source: Beat The GMAT — Problem Solving |
Rahul Lakhani
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Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Sorry, I am unable to understand your explanation.Rahul@gurome wrote:Fix one person in one place, so the permutations for the remaining 4 will be 4! = 4*3*2*1 = 24
[spoiler]The correct answer is (C).[/spoiler]
How is this question different from normal seating arrangement problem.
In normal seating arrangement problem answer would be 5!
-
GMATGuruNY
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Let's say that the 5 people are ABCDE.lokesh r wrote:Sorry, I am unable to understand your explanation.Rahul@gurome wrote:Fix one person in one place, so the permutations for the remaining 4 will be 4! = 4*3*2*1 = 24
[spoiler]The correct answer is (C).[/spoiler]
How is this question different from normal seating arrangement problem.
In normal seating arrangement problem answer would be 5!
If we were to count the ways to arrange ABCDE in a line, the following would qualify as different arrangements:
ABCDE
BCDEA
CDEAB
DEABD
EABCD
But when put around a table, all of the above would qualify as only one arrangement, because the clockwise order would always be the same: A-B-C-D-E. In all of the above, B would be directly to the right of A; C would be directly to the right of B; D would be directly to the right of C; and E would be directly to the right of D.
Thus, the number of ways to arrange N people around a circular table is smaller than the number of ways to arrange them in a line:
Number of ways to arrange N people around a circular table = (N-1)!.
So given 5 people, there are (5-1) = 4! = 24 ways to arrange them around a table.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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Thanks for the explanation..all these days i only knew formula..GMATGuruNY wrote:Let's say that the 5 people are ABCDE.lokesh r wrote:Sorry, I am unable to understand your explanation.Rahul@gurome wrote:Fix one person in one place, so the permutations for the remaining 4 will be 4! = 4*3*2*1 = 24
[spoiler]The correct answer is (C).[/spoiler]
How is this question different from normal seating arrangement problem.
In normal seating arrangement problem answer would be 5!
If we were to count the ways to arrange ABCDE in a line, the following would qualify as different arrangements:
ABCDE
BCDEA
CDEAB
DEABD
EABCD
But when put around a table, all of the above would qualify as only one arrangement, because the clockwise order would always be the same: A-B-C-D-E. In all of the above, B would be directly to the right of A; C would be directly to the right of B; D would be directly to the right of C; and E would be directly to the right of D.
Thus, the number of ways to arrange N people around a circular table is smaller than the number of ways to arrange them in a line:
Number of ways to arrange N people around a circular table = (N-1)!.
So given 5 people, there are (5-1) = 4! = 24 ways to arrange them around a table.
