Probability that the first card is a face card and the second is a diamond

2 cards are drawn from a shuffled deck of 52 cards without replacement,
determine the probability that the first card is a face card and the second is a diamond

P(1st card is a face card & diamond, 2nd card is another diamond)
= 3/52 * 12/51

P(1st card is a face card but not a diamond, 2nd card is a diamond)
= 9/52 * 13/51

P(1st card is a face card, 2nd card is a diamond)
= (3/52 * 12/51) + (9/52 * 13/51)
= 3/52
= 0.057692308