You draw cards from a standard -card deck without replacing them. What
is the probability that both cards are of the same suit?

For both cards in same suit, you must first select a suit -  4C1 = 4
  
From that selected suit you have to select 2 cards. Then definitly both cards are same suit.
So, it will be like this
  4C1 * 13C2

And we can get total number of combinations - 52C2
Answer will be given by division of these two values.
  (4C1 * 13C2)      4 * 78     4       12
  ------------ =   ------- =  ---- =  ----
      52C2           1326     17       51

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Pick 2 cards from 52 cards: 52C2 = 1326

Pick 2 cards from 13 cards of the same suit: 13C2 = 78

Let P(H) be the possibility of picking 2 heart cards: P(H) = 78/1326 = 1/17

Let P(X) be the possibility of picking 2 cards of the same
suits. Since we have 4 suits (heart, spade, diamond, club)
   P(X) = P(H) * 4 = 1/17 = 4/17
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The first card has a chance of 1 of being in some suit, and the second
should be 12/51 to be of the same suit, so the total is 12/51...