There are 11 people who can be the first place winner. Then for 
every one of those 11 people who can be the first place winner,
there remain 10 other people who can be the second place winner.

So that's 11×10 = 110 ways.

That's often written "11 Position 2" or 11P2, or the permutations of
11 things taken 2 at a time. Order matters because Tom getting 1st 
place and Harry getting 2nd place is different from Harry getting
1st place and Tom getting 2nd place.

Edwin