There are 60 pupil in a class.out of them 25 play football, 20 play hockey and30 cricket,12 play football and hockey 9 play hockey and cricket play cricket and football. 5 play all the games.Find how many of them play.
1) none of the games
2)only cricket
3)only football
Use Venn diagram.
In the intersection of all 3 circles, place 5
You need 9 in the intersection of hockey and cricket, but you already counted 5 of those. So place 4 in the intersection of hockey and cricket which is NOT part of the central part.
continue in this fashion ....
Just realized that you appear to be missing information, namely how many play cricket and football
Need to study
To find out how many pupils play none of the games, cricket only, and football only, we can use the principle of inclusion-exclusion.
1) None of the games:
To find the number of pupils who don't play any of the games, we need to subtract the total number of pupils playing at least one game from the total number of pupils in the class.
Total pupils in the class = 60
Pupils playing at least one game = P(Football) + P(Hockey) + P(Cricket) - P(Football and Hockey) - P(Hockey and Cricket) - P(Cricket and Football) + P(Football, Hockey, and Cricket)
Pupils playing at least one game = 25 + 20 + 30 - 12 - 9 - 5 + 5 = 54
So, the number of pupils who play none of the games = Total pupils in the class - Pupils playing at least one game = 60 - 54 = 6
2) Only cricket:
To find the number of pupils who play only cricket, we need to subtract the number of pupils playing more than one game from the total number of pupils playing cricket.
Pupils playing only cricket = P(Cricket) - P(Hockey and Cricket) - P(Cricket and Football) + P(Football, Hockey, and Cricket)
Pupils playing only cricket = 30 - 9 - 5 + 5 = 21
3) Only football:
To find the number of pupils who play only football, we need to subtract the number of pupils playing more than one game from the total number of pupils playing football.
Pupils playing only football = P(Football) - P(Football and Hockey) - P(Cricket and Football) + P(Football, Hockey, and Cricket)
Pupils playing only football = 25 - 12 - 5 + 5 = 13
Therefore, the answers are:
1) None of the games: 6 pupils
2) Only cricket: 21 pupils
3) Only football: 13 pupils