Find number of ways to place 10 people around circular table, so between two specific persons are exactly other two. For those two specific persons, we have 16 possible combinations, and $8!$ permutation for other 8 people. Is this right? I'm not sure because the table is circular.
Placing people around table
combinatoricsdiscrete mathematicspermutations
Best Answer
In a circular arrangement, only the relative order of the people matters.
Suppose the two specific persons are Anne and Barbara. Seat Anne. Barbara can either sit three seats to Anne's left or three seats to Anne's right. That ensures there are exactly two people between Anne and Barbara. Once Anne and Barbara are both seated, the remaining eight people can be seated in $8!$ ways as we proceed clockwise around the table from Anne. Hence, there are $$2 \cdot 8!$$ admissible seating arrangements.