Question: Twelve hundred students at δ rdek University were surveyed about the Summer Olympics: 620 wanted to watch pole vault, 730 wanted to watch gymnastics, and 460 were interested in the decathlon. Additionally, 170 wanted to watch the opening ceremonies and nothing else. It also turns out that 270 of the students favor both pole vault and decathlon, 330 students are fans of both pole vault and gymnastics, and 240 intend to view both gymnastics and decathlon. How many students like gymnastics or like decathlon? How many students want to watch all three sports?