Can I add a blog subfolder to my website and use a different theme

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The same WordPress install can only use one Theme at any one time. In order to have one Theme on {root} and a different Theme on {root}/blog, you would have to have either:

  1. Separate WordPress installs at {root} and {root}/blog
  2. A WordPress Multisite Network at {root}, with a subfolder-based network and a network site at {root}/blog