I want to use the facebook like button on the bottom of each article, but it's only available on my home-page. In the settings of my template I use: show facebook like button.

Display Tweet, Google+ or Like buttons in your posts to share them in social media.

Show Tweet button.
Show Google+ button.
Show Facebook Like button.

The Settings > Social Buttons option always applies regardless of the menu item or layout profile. Once it is activated it should show the icon/s below the Intro in a "Category Blog" or "Featured Articles" and below the full text when the article is displayed as a "Single Article".

the icons are active below the intro of a category blog and "featured articles", but not below the full text of a single article: www.mijnwebsiteuser15.ml/organisaties/de...cheldetocht-augustus (single article)
www.mijnwebsiteuser15.ml (featured article)

Sorry our fail, in single articles the socials are not available.
Please try this way:
Add a "hidden" menu with a blog of these article and then link to the article within the blog.

Thanks for the quick response, I try it with a hidden menu