# 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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