I too did the same mistake.
Flaw in the @Vasu's approach is that it counts some combinations repeatedly.
For example -
$Combination_1 = \{F_1, F_2,D_1,D_2,G_1,F_3\}$
$Combination_2 = \{F_1, F_3,D_1,D_2,G_1,F_2\}$
$Combination_1$ and $Combination_2$ are same but above approach counts them twice.