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Today is Angelina birthday. She invited four friends to her [#permalink]

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01 Feb 2006, 14:56

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33% (02:02) correct
67% (00:31) wrong based on 6 sessions

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Today is Angelina birthday. She invited four friends to her party: Barbara, Carol, Don, and Frank. Everyone will be seated on a round table. How many possible way can these people be seated if Don and Carol must always sit next to each other?

i got 12 too (after some serious thought).
My initial thought was 4! x 2, but because the tabe is circular, you have to realize that ABCDF is the same as BCDFA, so only the combinations of the three other guests matter: 3!, then multipy by 2, for the cases in which CD are switched.

Is there a more mathematical explanation for this, or an analagous real-world situation (the way the electing 3 officers out of 9 people is analagous to creating 3-digit number out of 9 digits)?
ie- what are other expamples of circular permutations that aren't so blatanly worded as "x people sitting in a circle"?