HP laptops that come with pre-installed Win7 have 4 primary patritiona already used up. It isn't enough to shrink the NTFS partition as in the good old days :)

This is how I did with my HP Pavilion g6 2131so:

1. Run the Windows installation as usual.
2. Make a bootable DVD, the USB variant doesn't detect any HDD (!).
3. Boot from the DVD.
4. Connect USB memory, at least 32GB in size. Can be flash or rotating.
5. Start Gparted.
6. Wipe the USB memory (or make room), copy the partitions Backup and HP_TOOLS to USB memory, make the Backup partition on USB bootable.
7. Execute the changes.
8. You might want to shut down and boot from the USB you just created.
9. And while you're at it, boot Windows to make sure it survived the shrink operation.
10. Boot from the DVD again, start Gparted.
11. Delete the partitions Backup and HP_TOOLS from HDD, shrink the large unnamed NTFS partition to whatever you like to have as Win7 space.
12. Execute the changes. This will take loong time.
13. Create an extended partition in the freed-up space, size shall be Backup+ HP_TOOLS+ swap.
14. Execute the changes.
15. Copy the partitions Backup and HP_TOOLS from USB to the extended partition, create swap partition in the space left in the extended partition, create an ext4 (primary) partition in the remaining free space.
16. Execute the changes. Again, this will take some time.
17. Reboot and select your fav OS from the GRUB menu.
18. Quit Gparted, start Mint installation with the option to select which partitions Mint shall use.