Woody Allen is a famous film director who also plays saxophone/the saxophone. According to the latest press reports, the Prime minister/Prime Minister is going to resign. They had a guide with them when they climbed Himalayas/the Himalayas. Did you pay much for to go to supermarket/the supermarket on your way home? We spent three weeks at Hyatt/the Hyatt. The service was excellent. Отметить артикль нужен или нет и почему?

Woody Allen is a famous film director who also plays the saxophone. (артикль употребляется музыкальными инструментами).

According to the latest press reports, the Prime minister is going to resign. (с должностями, которые может занимать только один человек в стране, артикль употребляется).

They had a guide with them when they climbed the Himalayas (артикль употребляется с горными системами).

Did you pay much for to go the supermarket on your way home? (артикль употребляется со словами, указывающими место нахождения, направление).

We spent three weeks at the Hyatt. The service was excellent. (артикль употребляется с названиями отелей).