I want to install a bathroom exhaust in a downstairs bathroom. The problem is that there is also the furnace and gas water heater in this room. They are not enclosed in any way. The room is around 100 sq/ft and is able to get plenty of fresh air from the rest of the basement, through the floor joists (no ceiling installed). Will I have a problem with the bathroom exhaust sucking out carbon monoxide from the hot water heater and/or the furnace? The exhaust fan would be roughly five feet away from the water heater and furnace.

Thank you for your help.

It is illegal to install a gas fired water heaters in bathrooms if u didn't know. If so u would have to use a sealed combustion water heater due to products of combustion, carbon monoxide, flue gases, etc. Or u must meet the 50 cubic ft per 1000btu input for proper and efficient operation of water heater.
If anything its good.

Please stop copying barely relevant information from other sites into all your answers.