One Theme on Main and a different theme on the Sub

Hi,
Is it possible to have one theme on the main site and install a different theme on the subdomain? with both using the same wordpress installation?

For instance I have business pro theme on the main site and I’ve just created a subdomain on which I’d like to use an auction theme. I’d like to point one of the pages on the main theme to this subdomain so that users can access the auction.
Thank you