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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
Solution
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`
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