	PG(3,2) arises as a background in some solutions of Kirkman's schoolgirl problem. Two of the seven non-isomorphic solutions to this problem can be embedded as structures in the Fano 3-space. In particular, a "spread" of PG(3,2) is a partition of points into disjoint lines, and corresponds to the arrangement of girls (points) into disjoint rows (lines of a spread) for a single day of Kirkman's schoolgirl problem. There are 56 different spreads of 5 lines each. A "packing" of PG(3,2) is a partition of the 35 lines into 7 disjoint spreads of 5 lines each, and corresponds to a solution for all seven days. There are 240 packings of PG(3,2), that fall into two conjugacy classes of 120 under the action of PGL(4,2) (the collineation group of the space); a correlation interchanges these two classes.