8. Three girls and a boy must sit around a table with five chairs, numbered from 1 to 5. To decide their seat, each of the four draws at random one of five slips of paper (numbered from 1 to 5). What is the probability that the empty chair will be between two girls?
(A) $3 / 5$
(B) $2 / 5$
(C) $2 / 3$
(D) $3 / 4$
(E) $1 / 2$
(8) The correct answer is $(E)$.

Considering only the gender of the 4 people (male or female), the total number of possible configurations is equal to 20: that is, 5 (corresponding to choosing one of the 5 chairs to leave empty) multiplied by 4 (the number of possible choices for the boy's seat, once the empty chair is decided). The number of favorable cases, i.e., where the empty chair is between two girls, is instead equal to 10: that is, 5 (as above) multiplied by 2 (corresponding, once the empty chair is fixed, to the number of possible choices for the boy's seat, not adjacent to that chair). The required probability is thus equal to $10 / 20 = 1 / 2$.

Question proposed by Matteo Rossi.