Co-prime positive integers, Mathematics

A group of 5 people are going to meet weekly at the library for 4 weeks. Every week, two people are selected at random to speak. Every person may speak in multiple weeks, but no pair of people will speak together more than once. The probability that there is a person who will never be asked to speak can be expressed as a/b where a and b are co-prime positive integers. What is the value of a+b?

 

 

 

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