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# How does circular combination change when one unit is fixed?

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How does circular combination change when one unit is fixed? [#permalink]  03 Oct 2014, 22:33
IE 7 seats around a circle, but one must sit in an individual spot. Say Just Must sit in Seat 1.

Then,

What if we say Jane Must sit by John?

Do we still use some variation of (n-1)! ?

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Re: How does circular combination change when one unit is fixed? [#permalink]  06 Oct 2014, 23:30
Expert's post
icyevo wrote:
IE 7 seats around a circle, but one must sit in an individual spot. Say Just Must sit in Seat 1.

Then,

What if we say Jane Must sit by John?

Do we still use some variation of (n-1)! ?

If one person sits on one particular seat, that seat becomes distinct and so do all others. Say, now each of the 6 remaining seats are distinct, one is immediately to the right of the occupied seat, another is immediately to the left, another is second to the right, another is second to the left, another is third to the right and one is third to the left of the occupied seat. So every seat is distinct. Now you can make 6 people sit on 6 distinct seats in 6! ways.
Now if John occupied the first seat and Jane must sit next to him, this can be done in 2 ways (either to his left or to his right). Now rest of the 5 people occupy rest of the 5 places in 5! ways.
So total number of ways = 2*5!
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Re: How does circular combination change when one unit is fixed?   [#permalink] 06 Oct 2014, 23:30
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