1. A non-transitory computer-readable recording medium having stored therein a program for causing a first computer to execute a process of determining an installation order in which a plurality of update programs corresponding to a plurality of pieces of software are to be installed in the first computer to update current versions of the plurality of pieces of software to updated versions, the process comprising: applying a function outputting an index representing a degree of likelihood that a version of a piece of software is installed in the first computer, to information related to a plurality of pieces of software installed in a plurality of known second computers, to calculate the index for each combination of current versions and updated versions of the plurality of pieces of software; and searching for the installation order satisfying a predetermined condition based on a total of the indices corresponding to possible combinations of the current versions and the updated versions when installing a plurality of update programs corresponding to the plurality of pieces of software one by one from a state in which versions of all of the plurality of pieces of software are the current versions to a state in which the versions of all of the plurality of pieces of software are the updated versions.