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# 6 persons seat themselves at round table. What is the

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Manager
Joined: 25 Aug 2004
Posts: 171
Location: MONTREAL
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6 persons seat themselves at round table. What is the [#permalink]  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
Current Student
Joined: 04 Jan 2005
Posts: 283
Location: Milan
Schools: Wharton, LBS, UChicago, Kellogg MMM (Donald Jacobs Scholarship), Stanford, HBS
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Kudos [?]: 138 [0], given: 3

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.

P.
Manager
Joined: 17 Dec 2004
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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

2/5.
_________________

Wish you all good luck
Bhimsen Joshi

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