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

1/210 is the probability that two  particular professors occupy the seats on  either side of the Vice Chancellor during the  conference.​

Step-by-step explanation:

15 professors have been invited for a round  table conference by Vice chancellor of a  university.

Hence total people = 15 + 1 = 16

16 people can sit in 15!  ways

2 particular professors occupy the seats on  either side of the Vice Chancellor => position of 3 people is fixed

remaining 13 professor can be arranged in 13! ways

Probability =   13!/15!  = 1 / ( 15 * 14)  =  1/210

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Answer 2

The probability that two particular professors occupy the seats on either side of the Vice Chancellor during the conference is 1/210.

Explanation:

Number of professors have been invited for a round table conference by Vice chancellor of a university = 15.  

Hence total people = 15 + 1 = 16

16 people can sit in 15! Ways  

2 professors will occupy the seats on either side of the Vice Chancellor hence position of 3 people is fixed  

Remaining 13 professor can be arranged in 13! Ways  

Probability =   13! /15!  = 1 / (15 * 14) = 1/210

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