The selected few

A school committee is to consist of 3 teachers and 3 parents, who are to be chosen as random from a group of 20 teachers and 100 parents. If half of the teachers and 80 of the parents are over 45 years old, find the probability that the committee has only one parent and one teacher that are older than 45.

The solution can be expressed as \( \dfrac{a}{b} \) for positive coprime integers \(a\) and \(b\). Enter the value of \( a + b \).

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