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Lined Up in a Row...

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 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?

(AHSME, 1989)

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