Row of Boys and Girls!

Discrete Mathematics Level pending

Suppose that 7 boys and 13 girls line up in a row. Let \(S\) be the number of places in the row where a boy and a girl are standing next to each other. For example, for the row \(GBBGGGBGBGGGBGBGGBGG \), we have \(S=12\). The average value of \(S\) (if all possible orders of these 20 numbers are considered) is close to which of the following natural numbers?

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