I have done this problem by substituting numbers
We have n!/2!(n-2)! = 190
or n(n-1)/2 = 190
n=20 satisfies the equation
Two members of a club are to be selected to represent the club at a national meeting. if there are 190 different possible selections of the 2 members, how many members does the club have?
I know I can just plug in answer choices in to the formula n!/(n-r)!*r!=190
but I saw a explanation on this problem where they showed this step
n!/(n-2)! = n(n-1)
How is this step possible ?