Let the number that watch the three games be x, then
50 - x watch hockey and basketball only
70 - x watch football and hockey only
45 - x watch football and basketball only
115 - (45 - x) - (50 - x) - x = 20 + x watch basketball only
195 - (70 - x) - (50 - x) - x = 75 + x watch hockey only
285 - (45 - x) - (70 - x) - x = 170 + x watch football only
50 do not watch any of the three games.
x + 50 - x + 70 - x + 45 - x + 20 + x + 75 + x + 170 + x + 50 = 500
480 + x = 500
x = 500 - 480 = 20
a.) therefore, 20 people watch all the three games.
b.) 20 + x + 75 + x + 170 + x = 265 + 3x = 265 + 3(20) = 265 + 60 = 325.
Therefore, 325 people watch exaclty one of the three games.