Question
Six teachers and six students have to sit round a circular table such that there is a teacher between any two students. The number of ways in which they can sit is
A.
$$6! \times 6!$$
B.
$$5! \times 6!$$
C.
$$5! \times 5!$$
D.
None of these
Answer :
$$5! \times 6!$$
Solution :
Six students $${S_1},{S_2},.....,{S_6}$$ can be arranged round a circular table in $$5 !$$ ways. Among these 6 students there are six vactant places, shown by dots $$\left( \bullet \right)$$ in which six teachers can sit in $$6 !$$ ways.
Hence, number of arrangement $$= 5 ! \times 6 !$$
Six students $${S_1},{S_2},.....,{S_6}$$ can be arranged round a circular table in $$5 !$$ ways. Among these 6 students there are six vactant places, shown by dots $$\left( \bullet \right)$$ in which six teachers can sit in $$6 !$$ ways.
Hence, number of arrangement $$= 5 ! \times 6 !$$