A group of 5 people are going to meet weekly at the library for 4 weeks. Each week, two people are selected at random to speak. Each 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?

Well probability!!1

i like it,,

okay we have 5 people here,

total pairs possible  is ⁵C₂ = 10

suppose 1 person will not speak then we can select that person in 5 ways

remaining pairs possible = ⁴C₂ = 6

Now as the pairs will be speaking for 4 weeks we have to ensure the same pair does not speaks!!

so total selections possible without any restrictions = ¹⁰C₄ 

and total favourable selections = 5  *  ⁶C₄

so i believe you can find out the probablity = Favourable / total

it comes out to be  = 5/14

sum = 5 + 14 = 19

thats my lucky number

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