You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.
So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:
C (m,n) = m! / (n! * (m -n)! )
=> C (50,30) = 50! / (30! (50 - 30)! ) = (50!) / [30! (50 - 30)!] = 50! / [30! 20!] =
= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.
