Amy Richards' movie collection occupies $\frac{5}{8}$ of her computer's hard drive. Her photography takes up $\frac{1}{6}$ of the drive. The operating system, application software, and miscellaneous files take up another $\frac{1}{12}$ of the drive. If her hard drive's capacity is $120$ gigabytes, how many gigabytes of free space remain on the hard drive?