Question

In a group of children, 45 play football out of which 30 play Football only, 28 play Hockey; 25 play Cricket, out of which 11 play C only. Further 7 play C and F but not Hockey; 5 play Football andHockey but not Cricket and 10 play Football and Cricket both. Represent above information by Venn diagram. Find i) How many play all the three games? ii) How many play hockey only? iii How many are there in the group?

Answer 1

We begin by defining what a venn diagram is.

Venn diagram - - > An illustration utilizing circles either overlapping or non overlapping to depict a relationship between a finite group of things.

CALCULATIONS :

FOOTBALL : total =45

football only =30
Football + cricket = 7
Football + hockey = 5
Football + hockey + cricket = 45 - (30 + 7 +5) = 45 - 42 = 3

CRICKET : Total = 25

Cricket only = 11
Cricket + football = 7
Cricket + football + hockey = 3
Cricket + hockey = 25 - (11+7+3) = 4

HOCKEY: Total = 28

Hockey + football = 5
Hockey + cricket = 4
Hockey + football + cricket = 3
Hockey only = 28 - (5 + 4 + 3) = 16

Total students :

Total = (football only + cricket only + hockey only) + (hockey and football + hockey and cricket + cricket and football) + (football + hockey + cricket)

(30 + 16 + 11) + (7 + 5 + 4) +3 = 76

76 students.

16 students play hockey only.

Find the representation in Venn diagram in the image :