Another way of looking at this is as follows:
Probability that the 1st card is a club = 13/52
Probability that the 2nd card is a club, given the 1st is a club is: 12/51
Probability that the 3rd card is a club, given the first 2 are clubs is: 11/50
Probability that the 4th card is a club, given the first 3 are clubs is: 10/49
Hence the overall probability that all four are clubs is the product of these = 13*12*11*10/(52*51*50*49)
This can be written as (13!/9!)/(52!/48!) = (13!/[9!*4!])/(52!/[48!*4!]) = nCr(13,4)/nCr(52,4) (or C(13,4)/C(52,4) using Chris's notation).