Answer:
There are either 23 or 27 countries in North America, depending on the definition. (One fewer if Trinidad and Tobago is counted with South America.)
The countries of North America, Central America, and the Caribbean are:
Canada
US
Mexico
Belize
Guatemala
Honduras
El Salvador
Nicaragua
Costa Rica
Panama
Cuba
Haiti
Dominican Republican
Jamaica
Bahamas
Trinidad and Tobago (coast of Venezuela)
Barbados
St Vincent and the Grenadines
Grenada
St. Kitts and Nevis
St. Lucia
Dominica
Antigua and Barbuda
The European countries of Denmark, France, the UK, and the Netherlands are in North America due to islands or territories:
Denmark: Greenland
France : St. Pierre and Miquelon, St. Barthelmy, St. Martin, Martinique, Guadeloupe
UK : Anguilla, Bermuda, Cayman Islands, British Virgin Islands, Montserrat, Turks and Caicos
Netherlands : Aruba, Curacao, Sint Eustatius, Sint Maarten, Saba