Question

# A school awarded 30 medals in tennis, 14 in carrom and 25 in badminton. If these medals were bagged by a total of 50 students and only 5 students got medals in all the three sports, then the number of medals received by students in exactly two of the three games is

A
30
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
24
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
9
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
18
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C 9Let T,C,B denote the sets of students who bagged medals in tennis, carrom and badminton respectively. ⇒n(T)=30;n(C)=14;n(B)=25 Also, n(T∪C∪B)=50;n(T∩C∩B)=5 Now, we know the formula: n(T∪C∪B)=n(T)+n(C)+n(B) −n(T∩C)−n(C∩B)−n(B∩T) +n(C∩B∩T) To find: Number of medals received by students in exactly 2 games. n(T∩C)+n(T∩B)+n(B∩C)=x(let) Inserting the values in the formula: 50=30+14+25−x+5 ⇒x=30+14+25+5−50=24 Number of medals received by students in exactly 2 games=n(T∩C)+n(T∩B)+n(B∩C)−3n(T∩B∩C)=24−3(5)=9 Hence, 9 students bagged exactly two out of three medals.

Suggest Corrections
1
Join BYJU'S Learning Program
Related Videos
n(A∪B∪C) = n(A) + n(B) + n(C) − n(A∩B) − n(B∩C) − n(C∩A) + n(A∩B∩C)
MATHEMATICS
Watch in App
Join BYJU'S Learning Program