Boys and Girls Line Up

[BMAD]

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. If all possible orders of these 20 people are considered, what is the average value of S? Can you generalize this result to a group of m boys and n girls?

[Yoruichi-san]

2nm/(m+n)

Don't have time to write the full derivation, but I calculated the probability that, taking any pair in the lineup, one would be a boy and one would be a girl, then calculated the expectation value by multiplying by the number of pairs (m+n-1).

[Barcallica]

7.5?

[bonanova]

9.1

Y-san has it.