Question

A college awarded 38 medals in football , 15 in basket ball 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 is​

Answer 1

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? Hence, number of men who received medals in exactly two of the three sports = 9.

Answer 2

$\huge{\bf{\underline{\underline{\green{Given :-}}}}}$

• A college awarded 38 medals in football , 15 in basket ball 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 is

$\huge{\bf{\underline{\underline{\green{To Find :-}}}}}$

• How many received medals in exactly two of the three sports is ?

$\huge{\bf{\underline{\underline{\green{Solution :-}}}}}$

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

$\huge{\bf{\underline{\underline{\green{Answer :-}}}}}$

Hence, the received medals in exactly two of the three sports is ‘ 9 ’ .