Answer
$\frac{1}{7,059,052}$
Work Step by Step
Because the order is not important, we can use the combination rule to determine the number of possibilities: $\frac{44!}{(44-6)!6!}=7,059,052$.
We also know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, therefore $P=\frac{1}{7,059,052}$.