45 or older!

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 members the are over 45 years old.

Note: The solution can be expressed as \( \frac{a}{b} \). Express your answer as \( a + b \).

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