Two members of a club are to be selected to represent the

[Guest]

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?

20
27
40
57
95

This is probably super easy but I don't seem to find the solution. Thanks!

[Mike]

Let's say n is the number of members in the club.

There are 190 ways to select 2 members out of n.

n! / (2! * (n-2)!) = 190

n * (n-1) = 190 * 2!

n * (n-1) = 380

380 = 2*2*5*19 = 20 * 19

Answer: A (20 members)

[StaceyKoprince]

You can also try the answer choices. Let's say you decide to start in the middle:

If there are 40 members and 2 are selected, you'd set up this equation:
40!/[2!38!] = (40*39*38!)/(2*38!) = 40*39/2 = 20*39. Eyeball it - does that equal 190? No, it's too big. Try a smaller number. And so on, until you get the right answer!