Gotta read good books. But that doesn't mean you can't skip a volume or two.

Consider the problem this way: Name the books according to the volume numbers $\rightarrow 1,2,3,...,10$

So, we need to choose $4$ numbers among $1,2,3,...,10$ such that no two are consecutive.

Now, there is a trick to find this out. Say, you choose $x_1, x_2, x_3 and x_4$ which are some numbers between $1$ to $10$ (inclusive)

Then, $1 \leq x_1 < x_2 < x_3 < x_4 \leq 10$ . And, the min. difference between $x_1$ and $x_2$ , $x_2$ and $x_3$ and $x_3$ and $x_4$ is $2$ .

So, we again have: $1 \leq x_1 < x_2 -1 < x_3 -2 < x_4 -3 \leq 7$ . Now, these numbers can be consecutive. So, we just need to choose $x_1, x_2 -1, x_3 -2, x_4 -3$ between 1 to 7 (inclusive). And, there are ${7 \choose 4}$ ways to do this.

Hence, the answer is ${7 \choose 4}$ = $\boxed {35}$

It is a simple solution. We will do it from the back side.

Say you have already selected 4 books. The number of remaining books on the shelf is now 6.

Put the 4 books back into the shelf. The books can only be put in the gaps (i.e =7)

Number of ways $= \frac{7!}{4! 3!}$ $= 35$