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Question

A college awarded 38 medals in football, 15 in basketball and 20 in cricket.  If these medals went to a total of 58 men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports?


Solution

Foot ball  F
Basket ball B
Cricket   C
N(F)=38,n(B)=15,n(c)=20
n(FBC)=3
n(FBC)=58
No. of students who received medals in exactly 2 of 3 sports is
n(FB)n(FC)n(BC)
We know that,
n(ABC)=n(A)+n(B)+n(C)n(CB)n(BC)n(BC)+n(FB)
 (FBC)=n(F)+n(B)+n(C)n(FB)n(FC)n(BC)+n(FBC)
 n(FB)+n(FC)+n(BC)=n(FBC)+n(F)+n(B)+(C)+n(FB)
=(58)+38+15+20+3
 n(FB)+n(FC)+n(BC)=18
 No. of students who received medals is exactly 2 out of 3 sports = 18
 

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