Since the game SET[R] was first introduced to the public in 1993, it has stimulated some interesting studies. While the game itself is rather straightforward, a plethora of decent mathematical questions lies beneath the surface. It is perhaps because the game ties in so closely with such an underlying mathematical term that its implications can be seen in many major fields of mathematics. This note introduces a generalized version of the game SET[R] in which there are n[m] cards, m is greater than or equal to 4, n is greater than or equal to 3, m is greater than or equal to n. Each card has m features and each feature has n options. A precise formula is presented for calculating the total number of SETs in a general deck.