Poker Probability (3 of a kind)

I'm having trouble trying to figure some of this problem out. I'll provide what I know under the question below.

What is the probability that a five card poker hand will contain three of a kind? (Note: This should not include a full house. That is three of one kind and two of another)

|S| = C(52,5) = 2,598,960

|T| = C(13,1) x C(4,3) x C(48,1) x C(44,1) = 109,824

I know that i'm having trouble with |T|. I've heard that all I have to do is multiply it by 1/2 but I do not know why. Someone please explain throughly. Thanks!

Final Answer will be |S|/|T| = 88/4165