Question

Among a group of students, 50 played cricket, 50 played hockey and 40 played volley ball. 15 played
both cricket and hockey, 20 played both hockey and volley ball, 15 played cricket and volley ball and 10
played all three. If every student played at least one game, find the number of students and how many
played only cricket, only hockey and only volley ball?

I need it soon​

Answer 1

Answer:

10 students played all three////////(1)

15 played cricket and hockey///////excluding that 10///////5 played only cricket and hockey

20 played hockey and volleyball///////excluding that 10.///////10 placed only hockey and volleyball

15 played cricket and volleyball....excluding that 10//////5 played only cricket and volleyball

5 played cricket and hockey and 5 played cricket and volleyball/////excluding these 5+5= 10 from total no. of children who only played cricket/////(2)

children who only played cricket = 50- 10-10= 30//////using (1)&(2)

5 played only both cricket and hockey//////10 played hockey and volleyball///////excluding these 5+10=15 from children who only played hockey/////(3)

children who only played hockey= 50-10-15=5.. 25/////using (1)&(3)

5 played both cricket and volleyball///////10 played hockey and volleyball//////excluding these 5+10=15 from total no. of children who only played volleyball/////(4)

total no. of children who only played volleyball////= 40-10-15= 15/////using (1)&(4)

therefore/////no.of children only played cricket=30

only volleyball= 15

only hockey= 25

total no. of children = 30+15+25= 45+25= 70