What is the probability of drawing 3 cards from a deck and drawing 3 diamonds?

My answer key says you should use the following method:

52C3= 22,100
13C3= 286

Answer: 286/22100

But I'm wondering why the following logic doesn't turn out the same answer:
52C3 = 22,100 (total ways to pick 3 cards)
13C1*12C1*11C1= 1716

Probability = 1716/22100

Using the 2nd method, you are simply choosing one card at a time rather than all 3 cards at once. What's the difference and why am I getting different answers?