It is the last problem of the AHSME competition 1988-1989 (question 30)
"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 $\text{GBBGGGBGBGGGBGBGGBGG}$ we have that $S=12$. The average value of $S$ (if all possible orders of these $20$ people are considered) is closest to
$\text{(A)}\ 9\qquad\text{(B)}\ 10\qquad\text{(C)}\ 11\qquad\text{(D)}\ 12\qquad\text{(E)}\ 13 $
(see this link for the source: http://www.artofproblemsolving.com/Wiki/index.php/1989_AHSME_Problems/Problem_30)
I can't find an exact solution, but i know the answer must be A:9 (after having programmed it the exact solution is 91/10)
I'm in the sixth year of secondary school if that gives an idea of my mathematics level. (and i've completed all the AHSME questions from 1985-1986 to 1994-1995 unless this one)