Daniel, William, Amanda, Eric, and Grace make a trip to see Super Bowl LVIII in Las Vegas

$($made possible by their generous CIS TA wages$).$ Before they$$re allowed to enter, the security

guard lines them up in alphabetical order and tells them the following: the first two people

must flip a coin to decide who gets to enter the stadium first. The winner of the match can

then enter, while the loser must stay to play the next person in line. The person who wins the

next match gets to enter second, while the loser must again stay to play the next person in line.

This process continues until there is only $1$ TA left, who enters last. In how many orders can

the $5$ TAs enter the stadium?