In a competition there are 18 competitors. Answer the following:
A) During the first day they're competing in three-man teams (total of 6 teams). How many ways are there to select the teams?
B) If the main sponsor of the event demands that the four best ranked players mustn't play in the same groups, how many ways can you then select the teams?
I've tried the following:
A) There are (18*17*16 + 15*14*13 + 12*11*10 +...+ 3*2*1) ways to select the teams, and if the order of the groups mattered we would just multiply that wit 6!
However,this gives me approximately 700,000 ways, whereas the correct number of ways according to the book is ~190,000,000
B) The four best players must each be in a different group. Therefore we "lock" their positions. (1*14*13 + 1*12*11 + 1*10*9 + 1*8*7 + 6*5*4 + 3*2*1) gives us the ways to select the teams, and if the order of the groups matters, we multiply that with 6!
Once again, this value is far too small according the the book. Either my calculations are way off or the book is wrong.