Assuming there are no ties
Answer:
980100
Step-by-step explanation:
Let's start with the boys(we could also start with girls, it doesn't matter).
We can "choose" one of 11 boys for the gold medal. That athlete can't win any more medals, so there are 10 boys left.
We can then "choose" one of the 10 boys remaining for the silver medal. That athlete can't win any more medals, so there are 9 boys left.
We can lastly "choose" one of the 9 boys remaining for the bronze medal.
That makes 11 possible choices for gold medal * 10 possible choices for silver medal * 9 possible choices for bronze medal = 990 possible choices(for boys).
We can do the exact same for the girls, leaving us with 990 possible choices for the girls.
We then multiply the possible choices together to get 990*990=980100 possible ways to hand out the six medals
