Probability and combinations

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venmic: Master | Next Rank: 500 Posts; Posts: 222; Joined: Mon Oct 13, 2008 4:04 pmFollowed by: 2 members; Thanked: 3 times

by venmic » Sun Jul 31, 2011 1:24 pm

If 5 noble knights are to be seated at a round table, then how many different ways can they be seated?

Can you please explain

should it not be 120 the answer is given as 24

let me know what you think

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Source: Beat The GMAT — Problem Solving | Sun Jul 31, 2011 1:24 pm

edge: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Sun Jun 26, 2011 5:45 pm; Thanked: 2 times

by edge » Sun Jul 31, 2011 1:27 pm

In the absence of any other information, 120 is the correct answer.

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venmic: Master | Next Rank: 500 Posts; Posts: 222; Joined: Mon Oct 13, 2008 4:04 pmFollowed by: 2 members; Thanked: 3 times

by venmic » Sun Jul 31, 2011 9:31 pm

edge wrote:In the absence of any other information, 120 is the correct answer.

i thought the same too but supposedly in circular perms you need to use n-1) ! not sure why
so the answer is 24

can anyone please advice

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Sun Jul 31, 2011 10:08 pm

venmic wrote:
edge wrote:In the absence of any other information, 120 is the correct answer.
i thought the same too but supposedly in circular perms you need to use n-1) ! not sure why
so the answer is 24

can anyone please advice

Hey,
Consider the following:
A,B,C,D,E
B,C,D,E,A
C,D,E,A,B
D,E,A,B,C
E,A,B,C,D
These 5 cases are considered distinct in linear arrangement. But in circular arrangement, aren't they same? They are same. So, every order in the circular permutation is counted 5 times in linear permutations. Hence, we divide the total number of linear arrangements with 5.
So, answer will be 5!/5 = 4!
This is exactly, how you generalize for circular permutations of 'n' items. It will be n!/n = (n-1)!

Cheers!

Things are not what they appear to be... nor are they otherwise

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naveen451: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Sat Jul 16, 2011 11:56 pmFollowed by: 1 member; Location: hyderabad; Thanked: 2 times

by naveen451 » Mon Aug 01, 2011 12:56 am

(n-1)! ways for circular permutations and
(n-1)!/2 ways for necklaces

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Aug 01, 2011 4:40 am

I posted about circular permutations here:

https://www.beatthegmat.com/seating-arra ... 85488.html

I posted about ring permutations here:

https://www.beatthegmat.com/counting-methods-t73853.html

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