Need confirmation regarding the solution of a simple probability question related to deck of cards? 
Example 5: Two cards are drawn from a deck of cards.
1 s t card is a club
B: 1 s t card is a 7
C: 2 n d card is a heart.
Find the following probabilities:
(a) P(A or B)
(b) P (B or A)
(c) P (A and C)

I can easily solve (a) and (b).   But for (c) the solution in my book is as follows-

But I think it is not right. Because if the first card is a club the only 51 cards would be remaining.  So it should be $$13\div52*13\div51$$.
Please correct me if I am wrong or the book solution is wrong. I just need confirmation regarding this question.
