JEE Main & Advanced
Mathematics
Permutations and Combinations
Question Bank
Self Evaluation Test - Permutations and Combinatioins
question_answer
Six teachers and sic students have to sit round a circular table such that there is a teacher between any two students. The number of ways I which they can sit is
A)\[6!\times 6!\]
B)\[5!\times 6!\]
C)\[5!\,\times 5!\]
D)None of these
Correct Answer:
B
Solution :
[b] 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 vacant places, shown by dots (.) in which six teachers can sit in 6! Ways. Hence, number of arrangement \[=5!\times 6!\]