ollysuper

We have 2 Americans and we can choose one of them to receive a medal. This can be done in 2 ways.

Choosing a Canadian to receive a medal:
We have 5 Canadians, and we can choose one of them to receive a medal. This can be done in 5 ways.

Choosing a third skater to receive a medal:
After selecting an American and a Canadian, we are left with 17 skaters (19 - 1 American - 1 Canadian). This can be done in 17 ways.

Thus, we have:2 (American's choice).×5(Canadian's choice)×17(third skater's choice)=170 ways
 

Since the balls are indistinguishable, we can think about this problem as placing 4 identical labels into 8 distinct boxes. The first label can be placed in any of the 8 boxes, the second label can be placed in any of the remaining 7 boxes, and so on.  So  8×7×6×5=1680​.

The square root of a complex number is another complex number whose square is equal to the given complex number. The square of i is −1, but there is no complex number whose square is i. Therefore, i does not have any square roots among the complex numbers.