There is a tournament in the college. 60 students registered their names to
participate. At the eleventh hour, 10 participants decided not to participate in any game
due to health issues and the remaining all registered students will take part in the tournament. Management has decided to conduct three indoor games GAME1, GAME2 and GAME3. 25 play GAME1, 26 play GAME3 and 26 plays GAME2. 12 plays GAME1 and GAME3, 9 plays GAME1 and GAME2 and 5 play GAME1, GAME2 and GAME3.
Find the number of students who play
(a) GAME2 and GAME3.
(b) GAME2 and GAME3 but not GAME1.
(c) GAME3 only
(d) GAME3 but not GAME2
Answers
Given : three indoor games GAME1, GAME2 and GAME3. 25 play GAME1, 26 play GAME3 and 26 plays GAME2. 12 plays GAME1 and GAME3, 9 plays GAME1 and GAME2 and 5 play GAME1, GAME2 and GAME3.
To find : (a) GAME2 and GAME3. , (b) GAME2 and GAME3 but not GAME1.
(c) GAME3 only , (d) GAME3 but not GAME2
Solution:
Total Students Registered = 60
Did not participate any game = 10
Game 1 = 25
Game 2 = 26
Game 3 = 26
Game1 & Game 2 = 9
Game1 & Game3 = 12
Game2 & Game3 = ?
Game1, Game2 and Game3 = 5
Total = Game1 + Game2 + Game3 - Game1 &2 - Game1&3 - Game2&3 + Game1,2&3 + none
60 = 25 + 26 + 26 - 9 - 12 - Game2&3 + 5 + 10
=> Game2&3 = 11
number of students who play Game2&Game3 = 11
Game2&Game3 but not game 1 = Game2&3 - Game1,2&3
= 11 - 5
= 6
number of students who play Game2&Game3 but not game 1 = 6
Game 3 only = Game3 - Game1&3 - Game2&3 + game1,2&3
= 26 - 12 - 11 + 5 = 8
number of students who play Game 3 only = 8
Game 3 but not game 2 = Game 3 - Game2&3 = 26 - 11 = 15
number of students who play Game 3 but not Game 2 = 15
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