Question

A college awarded 40 medals in handball and 22 in badminton. if these medals to a total of 60 men and only five men got medals in all the three sports, how many received medals in exactly of two of three sports.
urgent please answer​

Answer 1

Step-by-step explanation:

Let n(F)=number of medals awarded in football =40

n(B)=number of medals awarded in basketball =16

n(C)=number of medals awarded in cricket =20

n(F∩C∩B)=number of medals awarded in all three =2

Since all these medals go to 64 people

n(FU CU B)=64

We know that

n(FU CU B)=n(F)+n(C)+n(B)-n(F∩C)-n(F∩B)-n(C∩B)+n(F∩C∩B)

64 = 40+20+16-n(F∩C)-n(F∩B)-n(C∩B) +2

n(F∩C)+n(F∩B)+n(C∩B)=14

Now each of these n(F∩C),n(F∩B),n(C∩B) includes the people received all three medals also along with 2 medals

So number of people who received medals in exactly two of the three sports are

= [n(F∩C) - n(F∩C∩B)] +[n(F∩B) - n(F∩C∩B)]+[n(C∩B) - n(F∩C∩B)]

= n(F∩C)+n(F∩B)+n(C∩B) - 3 n(F∩C∩B)

=14 -3×2=14–6=8