Question

A college awarded 38 medals in volley ball,
15 in football and 20 in basket ball. The
medals awarded to a total of 58 players and
only 3 players got medals in all three sports.
How many received medals in exactly two
of the three sports?​

Answer 1

Let F,B,C be the sets of students who received medals in football, basketball, and cricket respectively.

n(F)=38

n(B)=15

n(C)=20

n(F∪B∪C)=58

n(F∩B∩C)=3

We know, n(F∪B∪C)=n(F)+n(B)+n(C)−n(F∩B)−n(B∩C)−n(F∩C)+n(F∩B∩C)

n(F∩B)+n(B∩C)+n(C∩F)=73−58+3=18

the number of students who received medals in exactly two of the three

sports is,

n(F∩B)+n(B∩C)+n(C∩F)−3×n(F∩B∩C)=18−9=9