Find m+n for integers

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Jenn randomly chooses a number $J$ from $1, 2, 3,\ldots, 19, 20$. Bela then randomly chooses a number $B$ from $1, 2, 3,\ldots, 19, 20$ distinct from $J$. The value of $B – J$ is at least $2$ with a probability that can be expressed in the form $\frac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

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The probability that a3064bf09537273b5d950a1237686a0f0d7c2cf8 is 2f960094315d60883495f9b74148e17487ee9584 by symmetry. The probability that 1d2983083a7377c9a50a901175688c15acb00cde is 8676d13412d3c49f683c316d1b75719702f52fe4 because there are 19 pairs: 874e449e78b99e59432e66a8713c6e4178e4ec4a.

The probability that b8f2fb1b05b2158031e6f1015c986daf0df15c6a is 654d1dcd27bf7c632258ae474fea5c5036a4113e

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