1 in a group of students, 65 play football, 45 play hockey, 42 play cricket,
20 play football and hockey, 25 play football and cricket, 15 play hockey
and cricket and 8 play all the three games. Find the number of students
in the group. (Assume that each student in the group plays atleast one
Answers
100 Students
Let us assume F,C and H for the students who play Football, Cricket and Hockey.
Given:
Number of students that play football (F) = 65 students
Number of students who play hockey (H) = 45 students
Number of students who play cricket (C) = 42 students
Number of students that play both football and cricket (F ∩ C) = 25 students
Number of students that play both hockey and cricket (H ∩ C) = 15 students
Number of students that play all the three games (F ∩ H ∩ C) = 8 students
Calculating the total number of students in the group:
Using (F U H U C):
= n(F) + n(H) + n(C) - n(F∩H) - n(F∩C) - n(H∩C) + n(F∩H∩C)
Substituting the values into the following formula we get:
= 65 + 45 + 42 -20 - 25 - 15 + 8
= 100 students
Therefore, the total number of students that are there in this group is 100 students.