There is a five volume dictionary among 10 books arranged in a shelf in random order. The probability that these volumes stands in increasing order from left to right not necessarily kept side by side is

10 books arranged in a shelf in random order.$n\left(S\right)=10!$

E=a five volume dictionary among 10 books arranged in a shelf stands in increasing order from left to right not necessarily kept side by side is

out of 10 places other 5 books can be arranged in ${ }^{10}{P}_5$ ways and 5 volume dictionaries can be arranged in ascending order in one way in the remaining places.

$n\left(E\right){=}^{10}{P}_5$

$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{10!}{5!}\times \frac{1}{10!}=\frac{1}{5!}=\frac{1}{120}$