Probability of books on a shelf

Ok, this one is giving me some problems:

Qu. On a bookshelf there are works by three authors, three volumes by Gilmore, three

volumes by Lawson and one volume by Patterson. If the books are placed at

random on the shelf, the probability that the volumes of the same author are

together is

A. $\displaystyle \frac{3}{70}$

B. $\displaystyle \frac{1}{140}$

C. $\displaystyle \frac{3}{140}$

D. $\displaystyle \frac{1}{70}$

E. $\displaystyle \frac{1}{35}$

I could find the probability that three books from Gilmore are together, the separate probability that the books from Lawson being together, but I don't know how to find the intersection between those two sets of probabilities... (Thinking)

P(3 Gilmore together) =$\displaystyle \frac{3!5!}{7!} = \frac{1}{7}$

P(3 Lawson together) = $\displaystyle \frac{1}{7}$

P(3 Lawson together and 3 Gilmore together) = $\displaystyle \frac{3!3!3!}{7!} = \frac{3}{70}$

Total probability = $\displaystyle \frac{1}{7} + \frac{1}{7} + \frac{3}{70} - P(intersections)$

How can I solve this?