In a class of 30 learners,17 play football,15 play volleyball,12 play rugby,9 play volleyball only and 3 play rugby only. All learners play at least one of the 3 sports. Use a Venn diagram to find the number of learners who play only volleyball and rugby?

1 Answer
Tessalsifi
Feb 28, 2018

1

Explanation:

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Since they all play at least one sport, the number of people who don't play football is #30 - 17 = 13#.
The "no football" category is divided in 3 categories :
#rarr# only volleyball : 9
#rarr# only rugby : 3
#rarr# both : #x#
So we have :
#9+3+x=13#
#12+x=13#
#x=13-12=1#

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