A group of k Vikings independently set out to make a new home. Each Viking has a copy of the same map, showing n islands. Each Viking decides to set sail for some random island. If two or more Vikings land on the same island, they have a battle. (No matter how many Vikings land on that island, it counts as one battle.)

(a) How many islands do we expect will be visited by Vikings?

(b) How many battles do we expect will occur?

(c) Do your solutions conrm the intuitive answer for the special case where there is only one island on the map? Or what if there's only one Viking? What answers do you get for 400 Vikings and 100 islands? (use a calculator for this last part)