Blog on both home page AND blog page

I want to display the 3 latest posts on the homepage and have a separate blog page that shows, say, 10 posts. Is it possible? At the moment I have it set up sort of how I want it to work but it's not perfect. I currently have the "display posts on" setting as static homepage and blog on separate page. So I have the blog page set as a page called blog and the homepage is not set as any specific page. This is showing the blog on the front page and on its own page. I don't know if this is a bug or a wordpress thing but it works, as I said, sort of how I want it. I just want some customisation between the homepage blog display and the blog page display.