It wouldn't be possible to specify an image set specifically for the home-page per sé, but Background Manager does offer some flexibility that would allow something similar to what you're asking.
You can select a default Image Set (the one containing the 3 images) in the main Settings page (Appearance -> Background).
Then, whilst editing the other Image Set (with 7 images), you can select every possible category in the Override by Category box -- this would take care of all the posts.
Finally, for all your pages, you can override the background Image Set whilst editing them - select the one containing the 7 images instead of the default one.
So after this, all pages and posts would be using the Image Set containing the 7 images. Any other page (front page, error page, etc), the one containing the 3 images.