Ten teams are playing in a basketball tournament. in the first round, the teams are randomly assigned to games 1, 2, 3, 4 and 5. in how many ways can the teams be assigned to the games?

The question is asking how many ways can ten team be randomly assigned to 5 games. They can be randomly assigned in nPrC 
r = n!/( n-r)! ways. 
 So we have that 10 teams can be randomly assigned to five games in 10C5 ways. 
 10C5 = 10!/ (10-5)! = 10!/ 5! = 30240 ways. So they can be arranged in 30240 ways.