Question

A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went   to a total 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

let x get exactly one mrdal 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

9 Students

Given:

Number of medals awarded for Football = 38 (F)

Number of medals awarded for Basketball = 15 (B)

Number of medals awarded for cricket = 20 (C)

Total number of medals that the college awarded to its students =  15 + 38 + 20 = 58 n(F U B U C)

n(F ∩ B ∩ C) = 38 - 15 - 20 = 3

We have to find:

a + b + c

Solving:

n(F U B U C)  = n(F) + n(B) + n(C) - n(F ∩ B) - n(B ∩  C) - n(F ∩  C) + n(F ∩  B ∩  C)

Substituting the values in this equation we get:

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

58 = 67 - a - b - c

a + b + c = 67 - 58

a + b + c = 9

Therefore, 9 students received medals in exactly two of the three sports.