# A popular problem by Brilliant Member

A Brilliant member named Billy Bob Joe posts $$n$$ problems, where $$n$$ is a positive integer. The probability that exactly three of those problems will become popular is $$n$$ times the probability that exactly two of those problems will become popular. As $$n$$ gets larger and larger, the probability that a problem posted by Billy Bob Joe will become popular approaches $$\frac{a}{b},$$ where $$a$$ and $$b$$ are coprime positive integers. Find $$a + b.$$

Details and Assumptions:

• Assume that the probabilities of each problem becoming popular are equal and independent of each other.
• A problem can only be either popular or not popular. In other words, the probability that a problem will become either popular or not popular is equal to 1.
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