1. A computer system, comprising: a plurality of computers; and a management computer for managing a cluster which includes the plurality of computers, wherein each of the plurality of computers has a first processor, a first memory coupled to the first processor, a storage device coupled to the first processor, and a first network interface coupled to the first processor, wherein the management computer has a second processor, a second memory coupled to the second processor, and a second network interface coupled to the second processor, wherein the plurality of computers constituting the cluster include a plurality of first computers each of which uses the storage device to execute a service and a plurality of second computers for taking over the service that is executed by one of the plurality of first computers that has failed, wherein the management computer includes: a backup obtaining module for obtaining a backup image from each of the plurality of first computers; and a restoration pair management module for generating a plurality of restoration pairs each of which is constituted of at least one first computer and at least one second computer, and selecting, for each of the plurality of restoration pairs, a common image to be restored to the at least one second computer included in the restoration pair, wherein the management computer holds server management information for managing hardware configuration information and software configuration information for each of the plurality of computers constituting the cluster, and wherein the restoration pair management module is configured to: refer to the server management information and sort the plurality of first computers into a plurality of groups of first computers by which a software configuration for providing the service is common, in a case where a change in the configuration of the cluster is detected; refer to the server management information and allocate at least one second computer to each of the plurality of groups based on the hardware configuration information of each of the plurality of first computers and the hardware configuration information of each of the plurality of second computers; generate at least one restoration pair for each of the plurality of groups by associating at least one first computer that is included in one group with at least one second computer that is allocated to the one group; determine the common image for each of the plurality of restoration pairs out of the backup image of the at least one first computer included in the restoration pair; and generate a piece of restoration pair management information that associates identification information of the restoration pair, identification information of the at least one first computer included in the restoration pair, identification information of the at least one second computer included in the restoration pair, and identification information of the common image of the restoration pair with one another.