The requirement that the tails are not consecutive means that
1 <= x1 < x2-1, x2 < x3-1, x3 < x4-1, ..., x14 < x15-1, x15 <= 60.
An equivalent set of inequalities is
1 <= x1 < x2-1 < x3-2 < x4-3 < ... < x14-13 < x15-14 <= 46,
so selecting the positions of the tails is equivalent to selecting the numbers x1, x2-1, x3-2, ..., x15-14
(but now without any restriction on adjacency),
which can be done in C(46,15) ways.