Question 18
At the end of a professional bowling tournament, the top $5$ bowlers have a play-off. First #$5$ bowls #$4.$ The loser receives $5$th prize and the winner bowls #$3$ in another game. The loser of this game receives $4$th prize and the winner bowls #$2.$ The loser of this game receives $3$rd prize and the winner bowls #$1.$ The winner of this game gets $1$st prize and the loser gets $2$nd prize. In how many orders can bowlers #$1$ through #$5$ receive the prizes?