Question 5
A group consists of five girls, denoted by $G_1,G_2,G_3,G_4,G_5$, and twelve boys. Seventeen chairs are arranged in a row. Seat the group so that all the following conditions hold:
1. Every chair has exactly one occupant.
2. From left to right, the girls occur in the order $G_1,G_2,G_3,G_4,G_5$.
3. At least three boys sit between $G_1$ and $G_2$.
4. At least one and at most four boys sit between $G_4$ and $G_5$.
How many such arrangements are there? Two arrangements are different if some chair has different occupants in them.
1. Every chair has exactly one occupant.
2. From left to right, the girls occur in the order $G_1,G_2,G_3,G_4,G_5$.
3. At least three boys sit between $G_1$ and $G_2$.
4. At least one and at most four boys sit between $G_4$ and $G_5$.
How many such arrangements are there? Two arrangements are different if some chair has different occupants in them.