The total probability of selecting 3 books and whose page number is less than or equal to 7 is $\left(\frac{7}{20}\right)^3$.
Total probability of selecting 3 books whose page number is less than 7 is $\left(\frac{6}{20}\right)^3$.
$\therefore$ Requiried probability $=\left(\frac{7}{20}\right)^3-\left(\frac{6}{20}\right)^3$
Hence, option (4) is correct.