Question

1)A college awarded 38 medals in football 15 in basket ball and 20 in cricket.If there medals went to a total of 58 man and and only 3 men got medals all the three sports.How many received medals in exactly two or three sports.
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Answer 1

Step-by-step explanation:

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

Answer 2

Step-by-step explanation:

n(F)=38

n(B)=15

n(C)=20

n(F∪B∪C)=58

n(F∩B∩C)=3

∵n(F∪B∪C)=n(F)+n(B)+n(C)−n(F∩B)−n(B∩C)−n(C∩F)+n(F∩B∩C)

n(F∩B)+n(B∩C)+n(C∩F)=n(F)+n(B)+F(C)+n(F∩B∩C)−(F∪B∪C)

=38+15+20+3−58=18