VMO 2012 - Insane

Given a group of five girls g1, g2, g3, g4, g5 and twelve boys. There are seventeen seats are arranged in a horizontal row. It grouped people who sit in that chair so that the following conditions are simultaneously satisfied:

a) Each have exactly one passenger seat;

b)The order of the girls, considered from left to right, are g1, g2, g3, g4, g5;

c) Between g1 and g2 have at least three boys;

d) Between g4 and g5 have at least one boy and four boys the most.

How many ways there are to arranged all the seats?

Two ways are considered different if there exists a chair that the person sitting in that chair is different in two ways ratings.

P/s : Sorry if it hard to understand :( i did try my best !~

#Combinatorics

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$