Question

On its annual sports day school awarded 35 medals in athletics 15 judo and 18 in swimming if the medals goes to a total of 58 students and only three of them got medals in all the three sports the number of students who received medals in exactly 2 of 3 sports are
(a) 9. (b) 4. (c) 5. (d) 7

Answer 1

let the no. of students got medal in 2or3 sport are x
total medals =35
judo. 15
swimming. 18
total students. 58
atq
35- 3(3) =24
35-(15+18)=2
2×3=6
24/6=4
ans is 4students

Answer 2

Given,

Total students = 58

Students who got medals in athletics = 35

Students who got medals in judo = 15

Students who got medals in swimming = 18

Students who got medals in all three = 3

To Find,

Students who got medals in exactly 2 sports =?

Solution,

Let the Students who got medals in athletics, judo and swimming be A, J and S respectively.

n(A) = 35

n(J) = 15

n(S) = 18

n(A ∪ J ∪ S) = 58

n(A ∩ J ∩ S) = 3

We know that,

n(A ∪ J ∪ S)=n(A)+n(J)+n(S) − n(A∩J)−n(J∩S)−n(S∩A) + n(n(A ∩ J ∩ S))

58 = 35 + 15 + 18 - n(A∩J)−n(J∩S)−n(S∩A)   + 3

n(A∩J)−n(J∩S)−n(S∩A) = 68 - 58 + 3 = 13

The number of students who got medals in exactly two of the three

sports are ,

n(A∩J)−n(J∩S)−n(S∩A) - 3 * n(A ∩ J ∩ S) = 13 - 3*3 = 13 - 9

n(A∩J)−n(J∩S)−n(S∩A) - 3 * n(A ∩ J ∩ S)  = 4

Hence, The number of students who got medals in exactly 2 of the 3 sports is 4. Option(b) is the correct answer.