VMO 2012 Problem 5

For a group of 5 girls, denoted as $G_1,G_2,G_3,G_4,G_5$ and $12$ boys. There are $17$ chairs arranged in a row. The students have been grouped to sit in the seats such that the following conditions are simultaneously met: (a) Each chair has a proper seat. (b) The order, from left to right, of the girls seating is $G_1; G_2; G_3; G_4; G_5.$ (c) Between $G_1$ and $G_2$ there are at least three boys. (d) Between $G_4$ and $G_5$ there are at least one boy and most four boys. How many such arrangements are possible?