Manny is the captain of the $15$ member soccer team that has won his city's championship. How many ways can Manny and $2$ other players line up to receive the championship trophy, if the captain must be first in line?
Here is what I have: Way 1: captain, Player 1, Player 2, Way 2: Captain, Player 2, Player 1. Answer $2! = 2 \times 1= 2$ ways, but I don't think this is correct.
Actually, the answer is $182$. There are $14$ choices for the first player after Manny and, for each such choice, $13$ choices for the second player. So, the answer is $14\times13$.