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# Boys and Girls Line Up

## Question

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?

## Recommended Posts

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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).

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7.5?

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9.1

Y-san has it.

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