Question

A college awarded 38 medals in football, 15 in basketball and 20 in

cricket. If these medals went to a total of 58 men and only three men got medals in all

the three sports, how many received medals in exactly two of the three sports ?​

Answer 1

Step-by-step explanation:

Correct option is

C

9

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