Posted by doug on Monday, March 14, 2011 at 8:12pm.
The number of ways is denoted (18,4), pronounced as "18 choose 4".
Basically, we would choose the first one from 18, second from 17,....
Since the choices are independent, the number of choices are multiplied together to get 18*17*16*15.
However, since the order of choices is not important, we have over-counted by 4*3*2*1 times, so the result should be divided by this factor, so
(18,4)=18*17*16*15/(1*2*3*4)
=(18!/14!)/4!
=18!/(14!4!)
where 18! means factorial 18.
In the general case,
(m,k)=m!/((m-k)!k!)