# Circular arrangement for twin pairs

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

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