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Question: Say, there is n number of twins. How many ways can they be seated at a round table if k pair of twins has to sit together?

Solution: I solved it in the following way. Is it correct?

If I subtract k pairs from 2n, total no. of people= 2n-k. This (2n-k) can be arranged in (2n-k-1)! ways.

Again k no. of pairs can be arranged in 2^k ways among themselves. So, total no. of ways= (2n-k-1)! * 2^k

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  • $\begingroup$ why are you subtracting 1? also, you have to account for the table being round $\endgroup$ – XRBtoTheMOON Nov 4 '17 at 7:26
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    $\begingroup$ as for circular arrangement, n objects can be arranged in (n-1)! ways $\endgroup$ – Mahmudul Hasan Nov 4 '17 at 7:29
  • $\begingroup$ ahhh, I see. I think that's right then. $\endgroup$ – XRBtoTheMOON Nov 4 '17 at 7:31
  • $\begingroup$ If you subtract $k$ pairs, you have $2n - 2k$ people left. $\endgroup$ – N. F. Taussig Nov 4 '17 at 8:48
  • $\begingroup$ Please clarify what you mean by $k$ pairs of twins sit together. Do you mean exactly $k$ pairs? $k$ particular pairs? at least $k$ pairs? $\endgroup$ – N. F. Taussig Nov 4 '17 at 10:09

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