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In how many ways can 6 people be arranged in a circle if a)

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In how many ways can 6 people be arranged in a circle if a) [#permalink] New post 25 Nov 2005, 15:26
In how many ways can 6 people be arranged in a circle if
a) 2 particular people are always together
b) if 2 particular people are always separated.
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Re: Permutations [#permalink] New post 25 Nov 2005, 16:39
a) 2 particular people are always together = 2(4!)
b) if 2 particular people are always separated= 5!-2 (4!)
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 [#permalink] New post 26 Nov 2005, 01:33
1) i got 2* 4! = 48

2) i got 6! - 2* 4! = 672
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 [#permalink] New post 26 Nov 2005, 03:42
I got the first one as 4! * 2 , but am not able to work out the second one Can someone please explain?
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Re: Permutations [#permalink] New post 27 Nov 2005, 08:31
sandman wrote:
In how many ways can 6 people be arranged in a circle if
a) 2 particular people are always together
b) if 2 particular people are always separated.


when there are mixed responses, OA and OE help clear the matter.

thanx
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 [#permalink] New post 27 Nov 2005, 08:49
6 ppl sit around one roundtable. number of comb is 5!.

when 2 ppl must sit together. take the 2 ppl as one unity. so its 4! comb. but the 2 ppl can change seats within the unity. its 4!*2.

when 2 ppl must not sit together. total com - 2 ppl must sit together. 5! - 4!*2.
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  [#permalink] 27 Nov 2005, 08:49
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