1. Lottery Odds Problem

I need help to work out the odds of winning a lottery

A Lottery ticket has 50 available blank selection boxes
The lottery player must enter in each of the 50 blank selection boxes either an up or down arrow.

At lottery draw time the winning 50, up and down arrow combination, is revealed.

every player that has the correct 50 combination wins. the lottery prize is not split if more than one player gets the correct 50 combination.

whats the odds of any one person getting the correct 50 combination, and could you explain to me how you arrive at the result?

2. $\displaystyle \Big(\frac{1}{2} \Big) ^{50}$ because there is a 50% chance of getting any one box correct, there are fifty boxes, and we assume each selection is independent of the other selections
4. Well, there are $\displaystyle 2^{50}$ possible combinations and only one of them is the winning combination.
So the odds are $\displaystyle 2^{50}-1 : 1$ which are extrememly low odds. Chances are fairly high that no one will win.