Question

15 professors have been invited for a round table conference by Vice chancellor of a university. What is the probability that two particular professors occupy the seats on either side of the Vice chancellor during the conference

Answer 1

15 professors and Vice-chancellor i.e., 16 persons can be arranged in a round table in (16 – 1)! = 15! ways

∴ n(S) = 15!

Let A ≡ the event that two particular professors are on either side of Vice-chancellor.

The two particular professors can occupy seats on either side of Vice-chancellor in ²P₂ = 2 ways.

After this the remaining 13 professors and 1 group of 2 particular professors and the Vice-chancellor, i.e., altogether 14 can be seated on a round table in (14 – 1)! = 13! ways.

∴ n((A) = 2 × 13!

∴ P(A) = `("n"("A"))/("n"("S"))`

= `(2 xx 13!)/(15!)`

= `(2 xx 13!)/(15 xx 14 xx 13!)`

= `1/105`