Cannot install OS X in recovery mode

Solution 1:

In Disk Utility each drive is represented by one line with indented lines underneath them for each partition (or volume) on that drive.

From the screenshots you provided, you are using a drive constellation Apple calls a Fusion drive. It consists of an SSD and a regular hard drive logically bundled together.

Disk Utility detects the logical volume group of that constellation, which is named "Macintosh HD" and by default there is a partition underneath it with the same name.

For some reasons, this is not the case for you and I also see that the partition buttons are greyed out. So, my suggestion is to intentionally break the Fusion constellation apart and have Disk Utility fix it thereafter. Here is how:

1. Close Disk Utility
2. Open Terminal (menu "Utilities")
3. Type in diskutil coreStorage list and look for the UUID (you will need it in the next step)
4. Type in diskutil coreStorage delete lvgUUID|lvgName where lvgUUID|lvgName is the UUID you found before
5. Quit Terminal after the command finished
6. Open Disk Utility and follow the on-screen instructions to fix the "damaged" disk

After that, you will be able to install OS X again.