Explanation
The command that installs GRUB 2 into the master boot record on the third hard disk is grub-install /dev/sdc.
The grub-install command is the high-level tool for installing GRUB 2 on a disk or a partition. It takes a device name as an argument and writes the GRUB 2 boot loader information to the specified location. If the device name is a disk, such as /dev/sdc, the boot loader information is written to the master boot record (MBR) of the disk, which is the first sector that contains the boot code and the partition table. If the device name is a partition, such as /dev/sdc1, the boot loader information is written to the boot sectorof the partition, which is the first sector of the partition that contains the boot code and the file system information. The grub-install command is part of the 101.1 Determine and configure hardware settings topic of the LPI Linux Essentials certification program12.
The other commands are either invalid or do not perform the desired task. The grub2 install command does not exist, as grub2 is not a valid command name. The grub-mkrescue command is used to create a bootable GRUB
2 rescue image, not to install GRUB 2 on a disk or a partition3. The grub-mbrinstall command does not exist, as mbrinstall is not a valid subcommand for grub. The grub-setup command is a low-level tool for installing GRUB 2 on a disk or a partition, but it is not recommended for normal use, as it requires specifying the location of the GRUB 2 core image file4. References:
* Linux Essentials - Linux Professional Institute Certification Programs1
* Exam 101 Objectives - Linux Professional Institute2
* GNU GRUB Manual 2.06: Making a GRUB bootable CD-ROM3
* GNU GRUB Manual 2.06: Installing GRUB natively4