Medals at the Olympics


New Member

I love sports and stats and so I am doing my Olympics research. I saw that there are 2 players from China's on each Badminton competition (MS, WS, MD, WD, XD). I calculated the chances of each winning the gold medal and then I calculated the chances of them winning 0, 1,2,3,4 or 5 medals.
Basically, I run all possible 32 combinations, I mean, using Pascal triangle I knew I had 1 option for 0 medals and 1 option for 5 medals, 5 combinations to win 1 or 4 medals and 10 combinations to win 2 or 3 medals. so 32 different combinations
6th Row of the Pascal Triangle. 1 5 10 10 5 1.
To make the math I just did it by hand, I mean I calculated all the 32 outcomes. It was not hard but still, isn't there a easier way ? Because I have other sports where I want to calculate the chances of CHI winning a gold medal but where I have more than just 5 different events!!

Also, how would you go if what you wanted to calculate was not the number of gold medals but rather the number of any medals ?

thank you.