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6 persons seat themselves at round table. What is the

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6 persons seat themselves at round table. What is the [#permalink] New post 08 Jan 2005, 08:09
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6 persons seat themselves at round table. What is the probability that 2 given persons are adjacent?



(A) 1/5
(B) 2/5
(C) 1/10
(D) 1/7
(E) 2/15
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Schools: Wharton, LBS, UChicago, Kellogg MMM (Donald Jacobs Scholarship), Stanford, HBS
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 [#permalink] New post 08 Jan 2005, 08:49
I'd go with B (2/5).

Simply, given any position for person A, person B is adjacent to A if s/he sits in 2 out of 5 places left around the table.

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 [#permalink] New post 08 Jan 2005, 10:14
Paradosso is right and the approach is simple.

One more approach which is not simple but holds many concepts is as follows...

A B C D E F be the six ppl and
A and B have to sit together.

Total # of ways n ppl can sit around a table is (n-1)!
therefore ppl can arrange themselves in (6-1)! equal to 5!
this becomes sample set.

Favourable events...
join two ppl so that they are one. That is they sit side by side.
Number of ways they can be arranged is 2. AB or BA ---1

Now these two ppl can be treated as one person. so this reduces # of ppl to 5.
AB C D E F
They can be arranged in (n-1)! ways that is (5-1)! ways. --2

Combining 1 and 2

2*4! is total number of favourable events

final answer 2*4!/5!
2/5.
_________________

Wish you all good luck
Bhimsen Joshi

  [#permalink] 08 Jan 2005, 10:14
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