## Problem of the Week

**Lined Up in a Row...**

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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?

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__AHSME, 1989__)