Which of the following is not a permitted installation method for receptacles within a countertop?

The appropriate method for installing receptacles within a countertop must adhere to safety standards and electrical codes. Option that indicates installation face down in a countertop is not permitted because it poses safety hazards. When receptacles are installed face down, it can lead to the risk of being covered by objects, allowing for potential water accumulation or spills to enter the receptacle, which can cause short circuits or electrical shock.

In contrast, receptacles installed face up are specifically designed to be listed for such an application, ensuring that they meet the necessary safety and functionality standards when used as intended on countertops. An installation at a slight angle is generally acceptable as it can still allow for safe access and operation while preventing the receptacle from being obscured. Lastly, using a GFCI device is a critical safety measure that protects against electrical shock, particularly in areas where water and electricity may intersect, such as kitchens.

Therefore, the only method that does not conform to safety and installation regulations for countertop receptacles is the face-down installation.