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# Factorial

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Manager
Joined: 24 May 2010
Posts: 83
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Kudos [?]: 25 [0], given: 1

Factorial [#permalink]  24 May 2010, 21:35
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Question Stats:

100% (01:22) correct 0% (00:00) wrong based on 0 sessions
Ok so if 5 people are to sit at a round table how many ways can they be seated. Why is the answer not 5!
Manager
Joined: 20 Apr 2010
Posts: 153
Location: I N D I A
Followers: 3

Kudos [?]: 17 [0], given: 16

Re: Factorial [#permalink]  24 May 2010, 23:07
Total No. of ways in which n no. of persons could be arranged on a round table is given by : ( n - 1 ) ! and not n !

Therefore the ans shd be 4! and not 5!
Manager
Joined: 24 May 2010
Posts: 83
Followers: 3

Kudos [?]: 25 [0], given: 1

Re: Factorial [#permalink]  25 May 2010, 06:03
Yes but why n-1 ! And not n! Can you give some more color so I can understand

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
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Re: Factorial [#permalink]  25 May 2010, 06:33
Expert's post
Jinglander wrote:
Yes but why n-1 ! And not n! Can you give some more color so I can understand

Posted from my mobile device

The number of arrangements of n distinct objects in a row is given by $$n!$$.
The number of arrangements of n distinct objects in a circle is given by $$(n-1)!$$.

From Gmat Club Math Book (combinatorics chapter):
"The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:

$$R = \frac{n!}{n} = (n-1)!$$"

$$(n-1)!=(5-1)!=24$$

Check Combinatorics chapter of Math Book for more (link in my signature).

Hope it helps.
_________________
Re: Factorial   [#permalink] 25 May 2010, 06:33
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