There are 10 students named alphabetically from A to J. What is the Probability that A and D do not sit together if all 10 sit around a circular table?\nOptions:\n(A) 2/9\n(B) 2/5\n(C) 7/9\n(D) 4/5\n(E) 8/9 Stream of consciousness first, then make a decision:
User
Number of students = 10\nNumber of ways 10 students can sit around a circular table = (10 - 1)! = 9!\nNumber of ways A and D sit together (consider A and D as one entity) = (9 - 1)! = 8! * 2\nNumber of ways A and D do not sit together = 9! - (8! * 2)\nProbability = (9! - (8! * 2))/9! = 1 - 2/9 = 7/9
Thus, the answer is (C).
Assistant