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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
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B
24
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C
9
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D
18
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Solution

The correct option is C 9
Let 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(TCB)=50;n(TCB)=5
Now, we know the formula:
n(TCB)=n(T)+n(C)+n(B)
n(TC)n(CB)n(BT)
+n(CBT)
To find: Number of medals received by students in exactly 2 games.
n(TC)+n(TB)+n(BC)=x(let)
Inserting the values in the formula:
50=30+14+25x+5
x=30+14+25+550=24
Number of medals received by students in exactly 2 games=n(TC)+n(TB)+n(BC)3n(TBC)=243(5)=9
Hence, 9 students bagged exactly two out of three medals.

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