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ICSE Class 8 Answered

In a school, 33 students are in a hockey team, 30 are in the football team and 33 in the cricket team. If 12 play hockey and cricket, 10 play cricket and football, 11 play hockey and football and 6 play all three games, find (i) how many students are there in all? (ii) how many play football only? (iii) how many play cricket only (iv) how many play hockey only?
Asked by parveenk_chaudhary | 22 Dec, 2018, 01:04: PM
answered-by-expert Expert Answer
No. of students play all games = 6
 
No. of students play Football and Cricket only  = No. of students paly Football and Cricket - No. of students paly all games = 10 - 6 = 4
No. of Students play Football and Hockey only = No. of students paly Football and Hockey - No. of students paly all games = 11 - 6 = 5
No. of students play Cricket and Hockey only   = No. of students paly Cricket and Hockey - No. of students paly all games   = 12 -6 =6
 
No. of Students play only football NF is calculated as follows
NF = No. of Stduents play football - No. of Students play Football and Cricket only - No. of Students play Football and Hockey only - No.of Students play all games
NF = 30-4-5-6 = 15
 
No. of Students play only Cricket NC is calculated as follows
NC = No. of Stduents play Cricket - No. of Students play Football and Cricket only - No. of Students play Cricket and Hockey only - No.of Students play all games
NC = 33-4-6-6 = 17
 
No. of Students play only Cricket NH is calculated as follows
NH = No. of Stduents play Hockey - No. of Students play Hockey and Cricket only - No. of Students play Hockey and Football only - No.of Students play all games
NH = 33-6-5-6 = 16
 
Assuming every student plays atleast one game, total number of students is obtained by adding all the numbers given in the venn diagram.
Total number of students = 69
 
Answered by Thiyagarajan K | 22 Dec, 2018, 03:37: PM

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