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Combinatorics Difficulty 3.0 AMC 10/12 Prove it United Kingdom

Three different numbers are chosen at random from the list $1, 3, 5, 7, 9, 11, 13, 15, 17, 19$ . The probability that one of them is the mean of the other two is $p$ . What is the value of $\frac{120}{p}$ ?

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