Question

la college awarded 38 medals in football , 15 in basketball and 20 in cricket if this medals went to a total of 50 men and only 5 men got medals in or three sports how many received medals in exactly two of the three sports​

Answer 1

Answer:

let x get exactly one medal and y get 2 medal and as stated 3 men get 3 medals.

therefore

x+2y+3*3=38+15+20=73

x+2y=64

also

x+y+3=58= total no. of participants

x+y=55

solving we get

y=9

Answer 2

Solution :

Let,

V = set of students getting medals in volleyball

F = set of students getting medals in football

B = set of students getting medals in basket ball

We are given the following:

n ( V ) = 38,

n ( F ) = 15

n ( B ) = 20

n ( V U F U B ) = 58

n ( V ∩ F ∩ B ) = 3

Let,

a = Number of students getting medals in volleyball and football but not the basketball

b = Number of students getting medals in football and basketball but not volleyball

c = Number of students getting medals in basketball and volleyball but not football

So,

n ( V U F U B ) is as follows :

⇒ [ 38 - ( a + c + 3 ) ] + [ 15 - ( a + b + 3 ) ] + [ 20 - ( b + c + 3 ) ] + a + b + c = 58

⇒ 67 - ( a + b + c ) = 58

⇒ a + b + c = 9

∴ Number of players who received medals in exactly two of the three sports,

⇒ a + b + c

⇒ 9

∴ Number of players who received medals in exactly two of the three sports is 9 respectively.