Question

In a class, 100 students play cricket ,120 play hockey and 150 play Tennis. For every 5 students who play cricket, there is one who plays cricket and hockey. For every 8 students who play Hockey there is one who plays hockey and Tennis. For every 10 students who play Tennis there is one who who plays cricket and Tennis . Ten students play all the three games and there are 20 who do not play any one of these games.
Q. How many students play at least one game?​

Answer 1

Answer:

Let ,F Hand C represent the set of students who play foot ball, hockey and cricket respectively. Then n(F)=65, n(H)=45, and n (C)=42.

n(F∩H)=20,n(F∩C)=25,n(H∩C)=15 and n(F∩H∩C)=8

We want to find the number of students in the whole group; that is n(F∩H∩C).

By the formula, we have

n(F∩H∩C)=n(F)+n(H)+n(C)−n(F∩H)−n(H∩C)−n(F∩C)+n(F∩H∩C)

65+45+42−20−25−15+8=100

Hence, the number of students in the group = 100.